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{ =}(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=(4-0)/(2-4)=(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