Given:
The graph of linear function.
To find:
The slope intercept form of the linear equation from the given graph.
Solution:
The slope intercept form of a linear function is:
[tex]y=mx+b[/tex]
From the given graph it is clear that the graph passes through the points (1,300) and (4,800).
The equation of line is
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
[tex]y-300=\dfrac{800-300}{4-1}(x-1)[/tex]
[tex]y-300=\dfrac{500}{3}(x-1)[/tex]
[tex]y-300=\dfrac{500}{3}x-\dfrac{500}{3}[/tex]
Adding 300 on both sides, we get
[tex]y=\dfrac{500}{3}x-\dfrac{500}{3}+300[/tex]
[tex]y=\dfrac{500}{3}x+\dfrac{900-500}{3}[/tex]
[tex]y=\dfrac{500}{3}x+\dfrac{400}{3}[/tex]
Therefore, the required equation is [tex]y=\dfrac{500}{3}x+\dfrac{400}{3}[/tex].
