Question

Determine the slope intercept form of the linear equation from its graph.​

Answer 1

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:

$y=mx+b$

From the given graph it is clear that the graph passes through the points (1,300) and (4,800).

The equation of line is

$y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)$

$y-300=\dfrac{800-300}{4-1}(x-1)$

$y-300=\dfrac{500}{3}(x-1)$

$y-300=\dfrac{500}{3}x-\dfrac{500}{3}$

Adding 300 on both sides, we get

$y=\dfrac{500}{3}x-\dfrac{500}{3}+300$

$y=\dfrac{500}{3}x+\dfrac{900-500}{3}$

$y=\dfrac{500}{3}x+\dfrac{400}{3}$

Therefore, the required equation is $y=\dfrac{500}{3}x+\dfrac{400}{3}$.