Question

Louis and Jenny each wrote an equation to represent the graphed linear function. Louis’s answer is y=2x. Jenny’s answer is y=x+2. Which student is correct?

Answer 1

Concept

First, find the slope of the line, and secondly use a slope-intercept form of the equation to find the equation of the line.

Step 1: find the slope

From the graph, choose two coordinates at the intercept

( 0, 2 ) and ( -2, 0 )

x1 = 0

y1 = 2

x2 = -2

y2 = 0

Substitute the values in slope equation

`\begin{gathered} \text{Slope m = }\frac{rise}{\text{run}}\text{ }=\text{ }(y_2-y_1)/(x_2-x_1) \\ \\ \text{Slope = }\frac{0-2}{-2-\text{ 0}} \\ \text{m = 1} \end{gathered}`

Step 2: Find the intercept c

The intercept on the y-axis is c = 2

Step 3: Write the equation of a line in slope-intercept form

y = mx + c

Step 4: substitute the values of m and c to find the equation

y = 1(x) + 2

y = x + 2

Final answer

y = x + 2 Jenny's is correct