Question

Allie and Roman are trying to graph the blue line shown on the left. Only one of them has a correct answer. Allie entered this equation: y=2x-8Roman entered this equation: y=8-2x Who is correct? Allie or Roman

Answer 1

Step 1

State the equation of a line in slope-intercept form

$\begin{gathered} y\text{ = mx + b} \\ or \\ y=\text{ b+mx} \end{gathered}$

The formula for the slope m is given as

$m\text{ =}\frac{y_2-y_1}{x_2-x_1}$

where

$\begin{gathered} y_2=4 \\ y_1=0 \\ x_2=2 \\ x_1=4 \end{gathered}$

Step 2

Find the slope

$m=\frac{4-0}{2-4}=\frac{4}{-2}=-2$

Step 3

Find the y-intercept, b

$\begin{gathered} \text{The y-intercept is found from the graph as 8} \\ \text{Hence, b = 8} \end{gathered}$

Step 4

Write out the equation

$\begin{gathered} y=-2x+8 \\ or \\ y=8-2x \end{gathered}$

Therefore, Roman is correct