Question 1

Determine whether the equation defines y as a linear function of x. If so, write it in the form y = mx + b .
4x = 7y  5
A) y =  x + 
B) y =  x - 
C) y = -  x - 
D) y = -  x + 
E)

Accepted Answer

The answer of Determine whether the equation defines y as...

Question 2

Find the slope of the line shown in the figure. 
A) 
B) 
C) 
D)

Accepted Answer

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

Question 3

Determine whether the equation defines y as a linear function of x. If so, write it in the form y = mx + b .
6x + 7y = 14
A) 
B) 
C) 
D) y is not a linear function of x.

Accepted Answer

The answer of Determine whether the equation defines y as...

Question 4

Metro Department Store's annual sales (in millions of dollars) during 5 years were  Plot the annual sales (y) versus the year (x) and draw a straight line L through the points corresponding to the first and fifth years and derive an equation of the line L.
A)  
B)  
C)

Accepted Answer

The answer of Metro Department Store's annual sales (in millions...

Question 5

Match each graph below with the letter of the corresponding slope description.
a.The slope of the line is zero.
b.The slope of the line is negative, and its y-intercept is negative.
c.The slope of the line is positive, and its x-intercept is positive.
-

Accepted Answer

The answer of Match each graph below with the letter...

Question 6

Metro Department Store's annual sales (in millions of dollars) during 5 years were  Plot the annual sales (y) versus the year (x) and draw a straight line L through the points corresponding to the first and fifth years and derive an equation of the line L.
A)   ​
B)   ​
C)   ​

Accepted Answer

- Plotting the given data points and drawing a line through the first and fifth years, we get a linear trend.
- The equation of a straight line can be given as y = mx + b, where m is the slope and b is the y-intercept.
- We can find the slope using the formula: m = (y2-y1)/(x2-x1), where (x1,y1) and (x2,y2) are two points on the line.
- Here, (x1,y1) = (1,11) and (x2,y2) = (5,11), so m = (11-11)/(5-1) = 0.
- Since the slope is 0, the line is horizontal and the equation is y = b, where b is the y-intercept.
- We can find the y-intercept by substituting any point on the line into the equation y = b. Using (1,11), we get:

11 = b

- Therefore, the equation of the line is y = 11.

Question 7

Sketch the straight line defined by the linear equation by finding the x- and y- intercepts. ​  ​
A) 
B) 
C) 
D) 
E)

Accepted Answer

To find the x-intercept, we set y = 0 and solve for x, which gives x = 3. To find the y-intercept, we set x = 0 and solve for y, which gives y = 4. Therefore, the line passes through the points (3, 0) and (0, 4), and has a slope of -4/3. The equation of the line in slope-intercept form is y = (-4/3)x + 4.

Question 8

Match each graph below with the letter of the corresponding slope description.
a.The slope of the line is undefined.
b.The slope of the line is positive, and its y-intercept is negative.
c.The slope of the line is negative, and its x-intercept is negative.
-

Accepted Answer

The answer of Match each graph below with the letter...

Question 9

Metro Department Store's annual sales (in millions of dollars) during 5 years were  Plot the annual sales (y) versus the year (x) and draw a straight line L through the points corresponding to the first and fifth years and derive an equation of the line L.
A)  
B)  
C)

Accepted Answer

The answer of Metro Department Store's annual sales (in millions...

Question 10

Sketch the straight line defined by the linear equation by finding the x- and y- intercepts. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Sketch the straight line defined by the...

Question 11

For the supply equation, where x represents the quantity supplied in units of 1,000 and p is the unit price in dollars, determine the number of units of the commodity the supplier will make available in the market at the given unit price. Please round your answer to the nearest unit. 3x - 5p + 30 = 0; p = 7
A) 1,567
B) 2,167
C) 1,667
D) 1,367

Accepted Answer

Substitute p = 7 into the supply equation:
3x - 5(7) + 30 = 0 
3x = 5(7) - 30 
3x = -5 
x = -5/3 
Since x represents the quantity supplied in units of 1,000, we need to multiply x by 1000 and round to the nearest unit:
x ≈ -1667
However, the quantity supplied cannot be negative, so we take the absolute value:
| -1667 | = 1667
Thus, the supplier will make 1667 units of the commodity available in the market at the price of $7. Rounded to the nearest unit, the answer is C: 1,667.

Question 12

For the demand equation, where x represents the quantity demanded in units of 1,000 and p is the unit price in dollars, determine the quantity demanded corresponding to the unit price p = 4. 4x + 5p - 40 = 0
A) 5,000
B) 3,500
C) 4,000
D) 4,500

Accepted Answer

4x + 5p - 40 = 04x + 5(4) - 40 = 04x + 20 - 40 = 04x = 20x = 5

Question 13

Match each graph below with the letter of the corresponding slope description.
a.The slope of the line is undefined.
b.The slope of the line is positive, and its y-intercept is negative.
c.The slope of the line is negative, and its x-intercept is negative.
-

Accepted Answer

The answer of Match each graph below with the letter...

Question 14

Match each graph below with the letter of the corresponding slope description.
a.The slope of the line is zero.
b.The slope of the line is negative, and its y-intercept is negative.
c.The slope of the line is positive, and its x-intercept is positive.
-

Accepted Answer

The answer of Match each graph below with the letter...

Question 15

Match each graph below with the letter of the corresponding slope description.
a.The slope of the line is zero.
b.The slope of the line is negative, and its y-intercept is negative.
c.The slope of the line is positive, and its x-intercept is positive.
-

Accepted Answer

The answer of Match each graph below with the letter...

Question 16

The relationship between temperature measured in the Celsius scale and the Fahrenheit scale is linear. The freezing point is  and  , and the boiling point is  and  , respectively. Find F as a function of C and use this formula to determine the temperature in Fahrenheit corresponding to temperature of  .
A) 
B) 
C) 
D)

Accepted Answer

The answer of The relationship between temperature measured in the...

Question 17

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. Suppose C(x) = cx + F and R(x) = sx are the cost and revenue functions of a certain firm. Then, the firm is making a profit if its level of production is less than  . 
A)a
B)b

Accepted Answer

The answer of Determine whether the statement is true or...

Question 18

Metro Department Store's annual sales (in millions of dollars) during 5 years were  Plot the annual sales (y) versus the year (x) and draw a straight line L through the points corresponding to the first and fifth years and derive an equation of the line L.
A)   ​
B)   ​
C)   ​

Accepted Answer

We plot the given data and draw a straight line passing through the points corresponding to the first and fifth years:

Year (x)     Sales (y)
1            11
2            eab
3            448
4            e894
5            2830

Using these two points, the slope of the line is:

m = (2830 - 11) / (5 - 1) = 704.75

Using the point-slope form of a line:

y - y1 = m(x - x1)

where (x1, y1) = (1, 11)

we get:

y - 11 = 704.75(x - 1)

Simplifying this equation, we get:

y = 704.75x - 693.75

Therefore, the best choice is B, which corresponds to the equation:

y = 704.75x - 693.75

Question 19

Match each graph below with the letter of the corresponding slope description.
a.The slope of the line is undefined.
b.The slope of the line is positive, and its y-intercept is negative.
c.The slope of the line is negative, and its x-intercept is negative.
-

Accepted Answer

The answer of Match each graph below with the letter...

Question 20

Entomologists have discovered that a linear relationship exists between the number of chirps of crickets of a certain species and the air temperature. When the temperature is  , the crickets chirp at the rate of  , and when the temperature is  , they chirp at the rate of  . Find N as a function of T and use this formula to determine the rate at which the crickets chirp when the temperature is  .
A) 
B) 
C) 
D)

Accepted Answer

The answer of Entomologists have discovered that a linear relationship...

Quiz 1: Straight Lines and Linear Functions

Determine whether the equation defines y as a linear function of x. If so, write it in the form y = mx + b . 4x = 7y 5

Find the slope of the line shown in the figure.

Determine whether the equation defines y as a linear function of x. If so, write it in the form y = mx + b . 6x + 7y = 14

Metro Department Store's annual sales (in millions of dollars) during 5 years were Plot the annual sales (y) versus the year (x) and draw a straight line L through the points corresponding to the first and fifth years and derive an equation of the line L.

Match each graph below with the letter of the corresponding slope description. a.The slope of the line is zero. b.The slope of the line is negative, and its y-intercept is negative. c.The slope of the line is positive, and its x-intercept is positive. -

Metro Department Store's annual sales (in millions of dollars) during 5 years were Plot the annual sales (y) versus the year (x) and draw a straight line L through the points corresponding to the first and fifth years and derive an equation of the line L.

Sketch the straight line defined by the linear equation by finding the x- and y- intercepts. ​ ​

Match each graph below with the letter of the corresponding slope description. a.The slope of the line is undefined. b.The slope of the line is positive, and its y-intercept is negative. c.The slope of the line is negative, and its x-intercept is negative. -

Metro Department Store's annual sales (in millions of dollars) during 5 years were Plot the annual sales (y) versus the year (x) and draw a straight line L through the points corresponding to the first and fifth years and derive an equation of the line L.

Sketch the straight line defined by the linear equation by finding the x- and y- intercepts.

For the demand equation, where x represents the quantity demanded in units of 1,000 and p is the unit price in dollars, determine the quantity demanded corresponding to the unit price p = 4. 4x + 5p - 40 = 0

Match each graph below with the letter of the corresponding slope description. a.The slope of the line is undefined. b.The slope of the line is positive, and its y-intercept is negative. c.The slope of the line is negative, and its x-intercept is negative. -

Match each graph below with the letter of the corresponding slope description. a.The slope of the line is zero. b.The slope of the line is negative, and its y-intercept is negative. c.The slope of the line is positive, and its x-intercept is positive. -

Match each graph below with the letter of the corresponding slope description. a.The slope of the line is zero. b.The slope of the line is negative, and its y-intercept is negative. c.The slope of the line is positive, and its x-intercept is positive. -

The relationship between temperature measured in the Celsius scale and the Fahrenheit scale is linear. The freezing point is and , and the boiling point is and , respectively. Find F as a function of C and use this formula to determine the temperature in Fahrenheit corresponding to temperature of .

Metro Department Store's annual sales (in millions of dollars) during 5 years were Plot the annual sales (y) versus the year (x) and draw a straight line L through the points corresponding to the first and fifth years and derive an equation of the line L.

Match each graph below with the letter of the corresponding slope description. a.The slope of the line is undefined. b.The slope of the line is positive, and its y-intercept is negative. c.The slope of the line is negative, and its x-intercept is negative. -

Sketch the straight line defined by the linear equation by finding the x- and y- intercepts.