Question 1

Provide an appropriate response.
-Find the line passing through the two points. Write the equation in standard form. (10, 9) and (10, 1)

Accepted Answer

Since both the given points have the same x-coordinate, the line passing through them must be a vertical line with equation x=10. This is the standard form of a vertical line. Since both points have the same x-coordinate of 10, the line connecting them is vertical and can be represented by the equation x = 10. This is the standard form for a vertical line.

Question 2

Provide an appropriate response.
-Find the standard form of the equation of the line with slope of  and passing through (4, 4).

Accepted Answer

The standard form of the equation of a line is Ax + By = C, where A, B, and C are integers and A is positive. We know the slope of the line is 11ebb17b_2a1a_91e1_afdc_15d202858e92_TB8591_11 and it passes through the point (4,4). Using point-slope form, we have:

y - y1 = m(x - x1)
y - 4 = 11ebb17b_2a1a_91e1_afdc_15d202858e92_TB8591_11(x - 4)

Multiplying out the slope and simplifying, we get:

y - 4 = 11ebb17b_2a1a_91e1_afdc_15d202858e92_TB8591_11x - 44
y = 11ebb17b_2a1a_91e1_afdc_15d202858e92_TB8591_11x - 40

To convert this to standard form, we rearrange the equation:

-11ebb17b_2a1a_91e1_afdc_15d202858e92_TB8591_11x + y = -40
Multiplying by -1:

11ebb17b_2a1a_91e1_afdc_15d202858e92_TB8591_11x - y = 40

Multiplying by a constant to make A positive and integers, we get:

2x + 7y = 36 (multiplying by -7)

Therefore, the answer is D. The standard form of the equation of a line is Ax + By = C, where A, B, and C are integers and A is positive. We are given the slope of the line, which is 11ebb17b_2a1a_91e1_afdc_15d202858e92_TB8591_11, and a point that the line passes through, (4,4). Using the point-slope form of the equation of a line, y - y1 = m(x - x1), we can substitute the slope and the point into the equation to get y - 4 = 11ebb17b_2a1a_91e1_afdc_15d202858e92_TB8591_11(x - 4). Simplifying this equation, we get y = 11ebb17b_2a1a_91e1_afdc_15d202858e92_TB8591_11x - 44 + 4, which becomes y = 11ebb17b_2a1a_91e1_afdc_15d202858e92_TB8591_11x - 40. To put this equation into standard form, we move the x-term to the left side and add 40 to both sides to get 2x + 7y = 36. Thus, the best choice is D.

Question 3

Provide an appropriate response.
-Find the slope of the line 3x + 4y = 11.

Accepted Answer

To find the slope of the line in the form Ax + By = C, we can rearrange the equation to solve for y: 4y = -3x + 11, y = (-3/4)x + 11/4. The coefficient of x (-3/4) is the slope of the line. Therefore, the slope is -3/4, which corresponds to choice B. The given equation can be rewritten as 4y = -3x + 11, or y = (-3/4)x + (11/4). The slope of this line is -3/4. Therefore, the correct answer is B, which represents -3/4 in decimal form.

Question 4

Provide an appropriate response.
-Find the line passing through the two points. Write the equation in standard form. (-3, 6) and (6, 6)

Accepted Answer

The y-coordinate for both points is the same (6), indicating a horizontal line. Therefore, the equation of the line is y = 6.

Question 5

Provide an appropriate response.
-Write the equation of a line that passes through (-1, 4) and (5, -1). Write the final answer in the form Ax + By = C where A, B, and C are integers with no common divisors (other than ±1) and A > 0.

Accepted Answer

First, find the slope (m) using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$, which gives $m = \frac{-1 - 4}{5 - (-1)} = \frac{-5}{6}$. Then, use point-slope form (y - y1 = m(x - x1)) with one of the points, say (-1, 4), to get the equation of the line. After rearranging to the required form, the equation becomes $5x + 6y = 19$.

Question 6

Write the slope-intercept equation (y = mx + b) for a line with the given characteristics.
-m = - 4, y-intercept (0, -7)

Accepted Answer

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. We are given that m = -4 and the y-intercept is (0,-7). 
Substituting these values into the slope-intercept form, we get: 
y = -4x - 7 We are given that the slope is -4 and the y-intercept is (0,-7). 
Using the slope-intercept form, we have:
y = mx + b 
y = -4x - 7 (Substitute m = -4 and b = -7) 
Therefore, option B is the correct answer.

Question 7

Provide an appropriate response.
-Graph the linear function defined by ion defined by f(x)  2 and indicate the slope and intercepts.

Accepted Answer

The answer of Provide an appropriate response.
-Graph the linear function...

Question 8

Write the slope-intercept equation (y = mx + b) for a line with the given characteristics.
-m = 3, passing through (1, -2)

Accepted Answer

Using the point-slope formula: y - y1 = m(x - x1) where (x1, y1) = (1, -2) and m = 3,
y - (-2) = 3(x - 1)
y + 2 = 3x - 3
y = 3x - 5
Thus, the slope-intercept equation is y = mx + b where m = 3 and b = -5, giving us choice A. Using the slope-intercept form (y = mx + b), we can plug in the given slope (m = 3) and the coordinates of the given point (1, -2) to solve for the y-intercept (b):
-2 = 3(1) + b
b = -5
Thus, the equation of the line is y = 3x - 5, which is choice A.

Question 9

Solve the problem.
-Using a phone card to make a long distance call costs a flat fee of $0.85 plus per $0.19 minute starting with the first minute. Find the total cost of a phone call which lasts 8 minutes.

Accepted Answer

The total cost is the sum of the flat fee and the cost per minute multiplied by the number of minutes.
Total cost = $0.85 + ($0.19 × 8) = $0.85 + $1.52 = $2.37.
Therefore, the best choice is C. The cost per minute is $0.19, so for an 8-minute call, the cost would be 8 x $0.19 = $1.52. Adding the flat fee of $0.85, the total cost of the call would be $0.85 + $1.52 = $2.37. Therefore, the correct answer is C.

Question 10

Provide an appropriate response.
-Write the equation of the line in the following graph.

Accepted Answer

The answer of Provide an appropriate response.
-Write the equation of...

Question 11

Find the slope of the line containing the given points.
-(-5, 2) and (0, 2)

Accepted Answer

The slope of a line is found by using the formula (y2-y1)/(x2-x1), where (x1,y1) and (x2,y2) are two points on the line. In this case, both points have a y-coordinate of 2, so the numerator is 2-2=0. The denominator is 0-(-5)=5, so the slope is 0/5=0. Therefore, the correct answer is A. The slope of a line passing through two points (x1,y1) and (x2,y2) is given by (y2-y1)/(x2-x1). In this case, both points have the same y-coordinate of 2, so the numerator is 2-2=0. The denominator is 0-(-5)=5. Therefore, the slope is 0/5, which simplifies to 0.

Question 12

Solve the problem.
-The cost for labor associated with fixing a washing machine is computed as follows: There is a fixed charge of $25 for the repairman to come to the house, to which a charge of $20 per hour is added. Find an equation that
Can be used to determine the labor cost, C, of a repair that takes x hours. Write the final answer in the form C =
Mx + b.

Accepted Answer

The fixed charge of $25 is added to $20 per hour. So, the equation that represents the total cost for x hours of work is:
C = 20x + 25
This is in the form C = Mx + b, where M = 20 and b = 25. Therefore, the best choice is C. For any repair that takes x hours, the fixed charge of $25 must be paid in addition to the labor charge of $20 per hour. Thus, the equation for the labor cost is:
C = 20x + 25
This equation is in the form C = Mx + b, where M is the slope (20) and b is the y-intercept ($25). Therefore, the correct answer is choice C.

Question 13

Graph the equation.
-

Accepted Answer

The answer of Graph the equation.
-
...

Question 14

Find the slope of the line containing the given points.
-(6, 1) and (6, - 4)

Accepted Answer

To find the slope of the line we use the formula:

slope = (y₂ - y₁) / (x₂ - x₁)

We have two points: (6, 1) and (6, -4)

Let's call the first point (x₁, y₁) and the second point (x₂, y₂)

So, we have:

x₁ = 6, y₁ = 1
x₂ = 6, y₂ = -4

Now we can plug these values into the formula:

slope = (y₂ - y₁) / (x₂ - x₁)
slope = (-4 - 1) / (6 - 6)

Notice that the denominator is 0, which makes the slope undefined. So the correct answer is D) Undefined. The slope of a vertical line is undefined because the change in x is 0. In this case, both points have an x-coordinate of 6, meaning there is no change in x, resulting in an undefined slope.

Question 15

Provide an appropriate response.
-Find the standard form of the equation of the line passing through the two points. (2, - 6) and (- 9, 6)

Accepted Answer

The answer of Provide an appropriate response.
-Find the standard form...

Question 16

Find the slope of the line containing the given points.
-(9, -7); (-6, 6)

Accepted Answer

The answer of Find the slope of the line containing...

Question 17

Provide an appropriate response.
-Use the graph to find the slope, x-intercept and y-intercept of the line.

Accepted Answer

- The slope can be found by using the rise over run formula: (change in y) / (change in x). From the graph, we can see that the line goes down one unit (rise) and right one unit (run), so the slope is -1.
- The x-intercept is where the line crosses the x-axis, which is at the point (7, 0) from the graph.
- The y-intercept is where the line crosses the y-axis, which is at the point (0, -7) from the graph. - The slope can be found by calculating the rise/run or delta y/delta x, which is -1/1 = -1.
- The x-intercept is the point where the line crosses the x-axis, which is (7, 0).
- The y-intercept is the point where the line crosses the y-axis, which is (0, -7).

Question 18

Solve the problem.
-The cost of manufacturing a computer part is related to the quantity produced, x, during a production run. When 100 parts are produced, the cost is $300. When 600 parts are produced, the cost is $4800. Find an equation
Of the line relating quantity produced to cost. Write the final answer in the form C = mx + b.

Accepted Answer

To find the equation of the line, we first calculate the slope (m) using the given points (100, 300) and (600, 4800). The slope m = (4800 - 300) / (600 - 100) = 4500 / 500 = 9. Then, using one of the points to solve for b in the equation C = mx + b, we get 300 = 9(100) + b, leading to b = 300 - 900 = -600. Thus, the equation is C = 9x - 600.

Question 19

Provide an appropriate response.
-Write the equation of a line that passes through (3, 9) and (0, -7). Write the final answer in the form Ax + By = C where A, B, and C are integers with no common divisors (other than ±1) and A > 0.

Accepted Answer

First, find the slope (m) using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$, which gives $m = \frac{-7 - 9}{0 - 3} = \frac{-16}{-3} = \frac{16}{3}$. Then, use point-slope form (y - y1 = m(x - x1)) with one of the points, say (3, 9), to get $y - 9 = \frac{16}{3}(x - 3)$. Simplify and rearrange to get $16x - 3y = 21$, which matches option B.

Question 20

Solve the problem.
-A small company that makes hand-sewn leather shoes has fixed costs of $320 a day, and total costs of $1200 per day at an output of 20 pairs of shoes per day. Assume that total cost C is linearly related to output x. Find an
Equation of the line relating output to cost. Write the final answer in the form C = mx + b.

Accepted Answer

The slope of the line is (1200 - 320) / (20 - 0) = 44. The y-intercept is 320. So the equation of the line is C = 44x + 320.

Quiz 1: Functions and Graphs

Provide an appropriate response. -Find the line passing through the two points. Write the equation in standard form. (10, 9) and (10, 1)

Provide an appropriate response. -Find the standard form of the equation of the line with slope of and passing through (4, 4) .

Provide an appropriate response. -Find the slope of the line 3x + 4y = 11.

Provide an appropriate response. -Find the line passing through the two points. Write the equation in standard form. (-3, 6) and (6, 6)

Provide an appropriate response. -Write the equation of a line that passes through (-1, 4) and (5, -1) . Write the final answer in the form Ax + By = C where A, B, and C are integers with no common divisors (other than ±1) and A > 0.

Write the slope-intercept equation (y = mx + b) for a line with the given characteristics. -m = - 4, y-intercept (0, -7)

Provide an appropriate response. -Graph the linear function defined by ion defined by f(x) 2 and indicate the slope and intercepts.

Write the slope-intercept equation (y = mx + b) for a line with the given characteristics. -m = 3, passing through (1, -2)

Solve the problem. -Using a phone card to make a long distance call costs a flat fee of $0.85 plus per $0.19 minute starting with the first minute. Find the total cost of a phone call which lasts 8 minutes.

Provide an appropriate response. -Write the equation of the line in the following graph.

Find the slope of the line containing the given points. -(-5, 2) and (0, 2)

Graph the equation. -

Find the slope of the line containing the given points. -(6, 1) and (6, - 4)

Provide an appropriate response. -Find the standard form of the equation of the line passing through the two points. (2, - 6) and (- 9, 6)

Find the slope of the line containing the given points. -(9, -7) ; (-6, 6)

Provide an appropriate response. -Use the graph to find the slope, x-intercept and y-intercept of the line.

Provide an appropriate response. -Write the equation of a line that passes through (3, 9) and (0, -7) . Write the final answer in the form Ax + By = C where A, B, and C are integers with no common divisors (other than ±1) and A > 0.