Question

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

Answer 1

Answer:

The equation of the line is:

$y = 28x$

Hence, option C is correct.

Step-by-step 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)

$\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

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

$m=\frac{280-224}{10-8}$

$m=28$

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.