Question

Which function has a greater slope and y-intercept than the linear function represented in the table?

A) y=2x+8.5
B) y=3x+7.5
C) y=5x+6.5
D) y=10x+5.5

Answer 1

B) y=3x+7.5

Explanation:

The equation of the data in the table can be obtained by using any two points.

We will use points (3, 13) and (5,17)

The slope - intercept form is:

• y = mx + b

We find the slope as:

• m = (17-13)/(5-3) = 4/2 = 2

The equation becomes:

• y = 2x + b

To find the value of b, the y -intercept is:

• 13 = 2*3 + b ⇒ b= 13 - 6 = 7

So the equation is:

• y = 2x + 7

Now let's compare this with the options

A) y = 2x + 8.5

• The slope is 2, and y- intercept is 8.5
• It has same slope and greater y-intercept
• Answer is no

B) y=3x+7.5

• The slope is 3, and y- intercept is 7.5
• It has greater slope and greater y-intercept
• Answer is yes

C) y=5x+6.5

• The slope is 5, and y- intercept is 7.5
• It has greater slope but smaller y-intercept
• Answer is no

D) y=10x+5.5

• The slope is 10, and y- intercept is 5.5
• It has greater slope but smaller y-intercept
• Answer is no