Answer:
[tex]y = \frac{1}{2}x - 2[/tex]
Step-by-step explanation:
Given
The attached graph
Required
Determine the linear equation
First, we need to calculate the slope
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
From the graph, the following relationships exist:
[tex](x_1,y_1) = (4,0)[/tex]
[tex](x_2,y_2) = (10,3)[/tex]
So, the expression for calculating slope becomes:
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m = \frac{3-0}{10-4}[/tex]
[tex]m = \frac{3}{6}[/tex]
[tex]m = \frac{1}{2}[/tex]
Next, we calculate the equation using:
[tex]y - y_2 = m(x - x_2)[/tex]
This gives:
[tex]y - 3 = \frac{1}{2}(x - 10)[/tex]
Open bracket
[tex]y - 3 = \frac{1}{2}x - 5[/tex]
Make y the subject:
[tex]y = \frac{1}{2}x - 5+3[/tex]
[tex]y = \frac{1}{2}x - 2[/tex]
