Question

Which equation represents the linear function that is shown on the graph below?

Answer 1

Answer:

$y = \frac{1}{2}x - 2$

Step-by-step explanation:

Given

The attached graph

Required

Determine the linear equation

First, we need to calculate the slope

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

From the graph, the following relationships exist:

$(x_1,y_1) = (4,0)$

$(x_2,y_2) = (10,3)$

So, the expression for calculating slope becomes:

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

$m = \frac{3-0}{10-4}$

$m = \frac{3}{6}$

$m = \frac{1}{2}$

Next, we calculate the equation using:

$y - y_2 = m(x - x_2)$

This gives:

$y - 3 = \frac{1}{2}(x - 10)$

Open bracket

$y - 3 = \frac{1}{2}x - 5$

Make y the subject:

$y = \frac{1}{2}x - 5+3$

$y = \frac{1}{2}x - 2$