Question 1

Write an equation of the line satisfying the given conditions. The line passes through (2, 9) and has a zero slope.
A) x = 2
B) y = 2
C) x = 9
D) y = 9

Accepted Answer

A line with a zero slope is horizontal, meaning all points on the line have the same y-coordinate. Since the line passes through (2, 9), the equation is y = 9.

Question 2

The figure represents the average credit card debt for selected households in Silerville.  Let y represent the credit card debt in dollars. Let x represent the year, where x = 0 corresponds to the year 1990, x = 4 represents 1994, and so on.
a. Use the ordered pairs given in the graph, (0, 3299) and (16, 7415) to find a linear equation to estimate the average credit card debt versus the year. Round the slope to the nearest tenth.
b. Use the model from (a) to estimate the average debt in 2003. Round to the nearest dollar.
c. Interpret the slope of the model in the context of this problem.

Accepted Answer

The answer of The figure represents the average credit card...

Question 3

A tool rental store charges a flat fee of $9.50 to rent a chain saw, and $3.75 for each day, including the first. Write an equation that expresses the cost y of renting this saw if it is rented for x days.
A) y = 9.50x + 3.75
B) y = 3.75x - 9.50
C) y = 3.75(x + 9.50)
D) y = 3.75x + 9.50

Accepted Answer

The cost y consists of a flat fee of $9.50 plus $3.75 per day for x days, which is represented by the equation y = 3.75x + 9.50.

Question 4

Write an equation of the line satisfying the given conditions. Write the answer inslope-intercept form. The line passes through $( 15,10 )$ and $( 0,10 )$.
A) $y = - \frac { 3 } { 4 } x + \frac { 15 } { 2 }$
B) $y = - \frac { 3 } { 4 } x - \frac { 15 } { 2 }$
C) $x = 10$
D) $y = 10$

Accepted Answer

The line passes through two points with the same y-coordinate (10), which means it is a horizontal line. The equation for a horizontal line is $y = k$, where $k$ is the constant y-value. Therefore, the correct equation is $y = 10$.

Question 5

The S-Cargo shipping company calculates shipping charges using the linear model y = 2.72x, Where y is the cost in dollars and x is the weight of the package in pounds $( 1 \leq x \leq 9 )$ . Use the linear Model to compute weight of a package with a shipping cost of $21.76. Round to the nearest Hundredth of a pound, if necessary.
A) 2.94 lb
B) 21.76 lb
C) 10.72 lb
D) 8.00 lb

Accepted Answer

To find the weight of the package, we use the given linear model $y = 2.72x$ and solve for $x$ when $y = 21.76$. Thus, $21.76 = 2.72x$. Solving for $x$, we get $x = \frac{21.76}{2.72} = 8$. Therefore, the weight of the package is 8.00 pounds.

Question 6

The following figure represents the average hourly wage for employees of MegaMart from 1980 to 2005.  Let y represent the hourly wage and let x represent the year, where x = 0 corresponds to the year 1980, X = 1 represents 1981, and so on. Then the average wage can be approximated by the equation Y = 0.17x + 3.02, where $0 \leq x \leq 25$ Use the linear equation to approximate the average wage for the year 1985 and compare it to the actual Wage of $3.75 per hour.
A) $4.72 per hour; the calculated wage was $0.97 more than the actual wage.
B) $3.02 per hour; the calculated wage was $0.73 less than the actual wage.
C) $3.02 per hour; the calculated wage was $0.17 more than the actual wage.
D) $3.87 per hour; the calculated wage was $0.12 more than the actual wage.

Accepted Answer

The answer of The following figure represents the average hourly...

Question 7

Write an equation of the line satisfying the given conditions. The line is perpendicular to the x-axis and passes through (-4, 8).
A) x = -4
B) y = -4
C) y = 8
D) x = 8

Accepted Answer

A line perpendicular to the x-axis is a vertical line, which means all points on the line have the same x-coordinate. Since the line passes through (-4, 8), the equation is x = -4.

Question 8

Write an equation of the line satisfying the given conditions. Write the answer in slope-intercept form. The line passes through $( 2,1 )$ and $( 3,18 )$.
A) $y = 17 x + 33$
B) $y = 19 x + 33$
C) $y = 19 x - 33$
D) $y = 17 x - 33$

Accepted Answer

First, calculate the slope (m) using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$, which gives $m = \frac{18 - 1}{3 - 2} = 17$. Then, use one of the points, say $(2,1)$, and the slope to find the y-intercept (b) using $y = mx + b$, which gives $1 = 17(2) + b$, solving for b gives $b = -33$. Thus, the equation is $y = 17x - 33$.

Question 9

Write an equation of the line satisfying the given conditions. Write the answer inslope-intercept form. The line contains the point $( 1,10 )$ and is parallel to $2 y - 12 x = 12$.
A) $2 y - 12 x = 10$
B) $y = 6 x + 4$
C) $y = 6 x + 6$
D) $y = 12 x + - 2$

Accepted Answer

First, we convert the given equation $2y - 12x = 12$ to slope-intercept form by solving for $y$: $y = 6x + 6$. A line parallel to this one will have the same slope, which is $6$. Using the point $(1,10)$ and the slope $6$, we can find the y-intercept ($b$) using the formula $y = mx + b$, leading to $10 = 6(1) + b$, thus $b = 4$. Therefore, the equation is $y = 6x + 4$.

Question 10

Write an equation of the line satisfying the given conditions. Write the answer inslope-intercept form. The line contains the point $( - 3 , - 4 )$ and is perpendicular to a line with a slope of $\frac { 3 } { 5 }$.
A) $y = - \frac { 5 } { 3 } x - 3$
B) $y = - \frac { 5 } { 3 } x - 9$
C) $y = - \frac { 5 } { 3 } x - 4$
D) $y = \frac { 5 } { 3 } x - 9$

Accepted Answer

The slope of the line perpendicular to a line with a slope of $ \frac{3}{5} $ is $ -\frac{5}{3} $ (negative reciprocal). Using the point-slope form $ y - y_1 = m(x - x_1) $ with $ m = -\frac{5}{3} $ and $ (x_1, y_1) = (-3, -4) $, we get $ y + 4 = -\frac{5}{3}(x + 3) $. Simplifying, $ y = -\frac{5}{3}x - 4 - 5 = -\frac{5}{3}x - 9 $.

Question 11

Write an equation of the line satisfying the given conditions. Write the answer inslope-intercept form. The line is perpendicular to the line defined by y = 4x - 8 and passes through the point(8, 3). 
A) $ y=-\frac{1}{4} x+5 $
B) $ y=\frac{1}{4} x+5 $
C) $ y=-\frac{1}{4} x-5 $
D) $ y=-4 x-5 $

Accepted Answer

The slope of the line perpendicular to $y = 4x - 8$ is $-\frac{1}{4}$ (negative reciprocal of 4). Using the point (8, 3) to solve for $b$ in $y = mx + b$, we get $3 = -\frac{1}{4}(8) + b$, leading to $b = 5$. Thus, the equation is $y = -\frac{1}{4}x + 5$.

Question 12

Write an equation of the line satisfying the given conditions. Write the answer in slope-intercept form. The line passes through $( 4,1 )$ and $( 2,9 )$.
A) $y = - 4 x + 15$
B) $y = - 4 x - 17$
C) $y = - 4 x + 17$
D) $y = 4 x + 15$

Accepted Answer

The slope of the line passing through the points $( 4,1 )$ and $( 2,9 )$ is $$m = \frac{9-1}{2-4} = -4$$Using the point-slope form of a linear equation, we have:$$y - 1 = -4(x - 4)$$Simplifying this equation to slope-intercept form, we get:$$y = -4x + 17$$

Question 13

A tool rental store charges a flat fee of $4.00 to rent a chain saw, and $5.25 for each day, including the first. Use a linear equation to find the cost of renting the saw for one week.
A) $9.25
B) $40.75
C) $36.75
D) $35.50

Accepted Answer

The cost of renting the saw for one week (7 days) can be calculated using the linear equation: Total cost = Flat fee + (Daily rate * Number of days). Thus, Total cost = $4.00 + ($5.25 * 7) = $4.00 + $36.75 = $40.75.

Question 14

Write an equation of the line satisfying the given conditions. The line passes through (-9, -6) and has an undefined slope.
A) y = -9
B) x = -9
C) y = -6
D) x = -6

Accepted Answer

A line with an undefined slope is a vertical line, which means all points on the line have the same x-coordinate. Since the line passes through (-9, -6), the equation of the line is x = -9.

Question 15

Write an equation of the given line in slope-intercept form.  
A) $y = 3 x - 4$
B) $y = - 4 x - 3$
C) $y = - 4 x + 3$
D) $y = - 3 x - 4$

Accepted Answer

The answer of Write an equation of the given line...

Question 16

Write an equation of the line satisfying the given conditions. The line passes through (-6, -9) and (-6, -11).
A) x = -6
B) y = -6x
C) y = 6
D) y = -6

Accepted Answer

The line has a constant x-value (-6) and varying y-values, indicating it is vertical. Vertical lines are represented by equations of the form x = k, where k is the x-value all points on the line share.

Question 17

Write an equation of the line satisfying the given conditions. Write the answer inslope-intercept form. The line contains the point $( - 6,19 )$ and is parallel to a line with a slope of $- \frac { 5 } { 2 }$.
A) $y = - \frac { 5 } { 2 } x - 6$
B) $y = - \frac { 5 } { 2 } x + 19$
C) $y = \frac { 5 } { 2 } x + 4$
D) $y = - \frac { 5 } { 2 } x + 4$

Accepted Answer

The line parallel to another line will have the same slope. Thus, the slope is $-\frac{5}{2}$. Using the point-slope form $y - y_1 = m(x - x_1)$ with point $(-6, 19)$, we get $y - 19 = -\frac{5}{2}(x + 6)$. Simplifying, we find the equation in slope-intercept form is $y = -\frac{5}{2}x + 4$.

Question 18

A tool rental store charges a flat fee of $7.00 to rent a chain saw, and $6.75 for each day, including the first. If you need to rent the saw and absolutely refuse to spend more than $74.50, what's the Maximum number of days you can keep the saw?
A) 14 days
B) 10 days
C) 5 days
D) 7 days

Accepted Answer

The total cost of renting the saw is made up of the flat fee plus the daily charge multiplied by the number of days. To find the maximum number of days, we set up the equation: $7.00 + $6.75 * number of days <= $74.50. Solving for the number of days gives us a maximum of 10 days within the budget.

Question 19

Write an equation of the line satisfying the given conditions. The line is parallel to the x-axis and passes through (9, 4)
A) x = 4
B) y = 4
C) y = 9
D) x = 9

Accepted Answer

Lines parallel to the x-axis have a constant y-value. Since the line passes through (9, 4), the equation is y = 4.

Question 20

The S-Cargo shipping company calculates shipping charges using the linear model y = 2.71x, Where y is the cost in dollars and x is the weight of the package in pounds $( 1 \leq x \leq 11 )$ . Use the linear Model to compute the shipping cost for a package weighing 2 lb. Round to the nearest cent.
A) $0.74
B) $5.42
C) $2.00
D) $4.71

Accepted Answer

To find the shipping cost for a package weighing 2 lb, substitute $x = 2$ into the linear model $y = 2.71x$. Thus, $y = 2.71 \times 2 = 5.42$. Therefore, the shipping cost is $5.42.

Quiz 2: Linear Equations in Two Variables and Functions

Write an equation of the line satisfying the given conditions. The line passes through (2, 9) and has a zero slope.

A tool rental store charges a flat fee of $9.50 to rent a chain saw, and $3.75 for each day, including the first. Write an equation that expresses the cost y of renting this saw if it is rented for x days.

Write an equation of the line satisfying the given conditions. Write the answer inslope-intercept form. The line passes through $( 15,10 )$ and $( 0,10 )$ .

Write an equation of the line satisfying the given conditions. The line is perpendicular to the x-axis and passes through (-4, 8) .

Write an equation of the line satisfying the given conditions. Write the answer in slope-intercept form. The line passes through $( 2,1 )$ and $( 3,18 )$ .

Write an equation of the line satisfying the given conditions. Write the answer inslope-intercept form. The line contains the point $( 1,10 )$ and is parallel to $2 y - 12 x = 12$ .

Write an equation of the line satisfying the given conditions. Write the answer inslope-intercept form. The line contains the point $( - 3 , - 4 )$ and is perpendicular to a line with a slope of $\frac { 3 } { 5 }$ .

Write an equation of the line satisfying the given conditions. Write the answer inslope-intercept form. The line is perpendicular to the line defined by y = 4x - 8 and passes through the point(8, 3) .

Write an equation of the line satisfying the given conditions. Write the answer in slope-intercept form. The line passes through $( 4,1 )$ and $( 2,9 )$ .

A tool rental store charges a flat fee of $4.00 to rent a chain saw, and $5.25 for each day, including the first. Use a linear equation to find the cost of renting the saw for one week.

Write an equation of the line satisfying the given conditions. The line passes through (-9, -6) and has an undefined slope.

Write an equation of the given line in slope-intercept form.

Write an equation of the line satisfying the given conditions. The line passes through (-6, -9) and (-6, -11) .

Write an equation of the line satisfying the given conditions. Write the answer inslope-intercept form. The line contains the point $( - 6,19 )$ and is parallel to a line with a slope of $- \frac { 5 } { 2 }$ .

A tool rental store charges a flat fee of $7.00 to rent a chain saw, and $6.75 for each day, including the first. If you need to rent the saw and absolutely refuse to spend more than $74.50, what's the Maximum number of days you can keep the saw?

Write an equation of the line satisfying the given conditions. The line is parallel to the x-axis and passes through (9, 4)

The S-Cargo shipping company calculates shipping charges using the linear model y = 2.71x, Where y is the cost in dollars and x is the weight of the package in pounds $( 1 \leq x \leq 11 )$ . Use the linear Model to compute the shipping cost for a package weighing 2 lb. Round to the nearest cent.