Question

Based on the data table, which equation accurately represents the situation?

A. y =8x + 224
B. y = 224x
C. y = 28x
D. y = 0.04x

Answer 1

The equation of the line is:

`y = 28x`

Hence, option C is correct.

Explanation:

The slope-intercept form of the line equation

y = mx+b

where

• m is the slope

• b is the y-intercept

Given the table

Gallons Miles Driven

8 224

10 280

4 112

Finding the slope between any two points, let say (8, 224) and (10, 280)

`\mathrm{Slope}=(y_2-y_1)/(x_2-x_1)`

`\left(x_1,\:y_1\right)=\left(8,\:224\right),\:\left(x_2,\:y_2\right)=\left(10,\:280\right)`

`m=(280-224)/(10-8)`

`m=28`

now substituting (8, 224) and m = 28 in the slope-intercept form of line equation

`y = mx+b`

224 = 28(8) + b

224 = 224 + b

b = 0

Thus, the y-intercept b = 0

now substituting b = 0 and m = 28 in the slope-intercept form of line equation

`y = mx+b`

`y = 28x+0`

`y = 28x`

Therefore, the equation of the line is:

`y = 28x`

Hence, option C is correct.