Answer:
[tex]y=-\dfrac{5}{4}x+4[/tex]
Step-by-step explanation:
The formula for the slope-intercept form of a linear equation is:
[tex]\boxed{\begin{array}{l}\underline{\textsf{Slope-intercept form of a linear equation}}\\\\y=mx+b\\\\\textsf{where:}\\\phantom{ww}\bullet\;\;\textsf{$m$ is the slope.}\\\phantom{ww}\bullet\;\;\textsf{$b$ is the $y$-intercept.}\\\end{array}}[/tex]
To write the equation of the graph line, first find its slope (m) by substituting two points on the line into the slope formula. Let's use points (-4, 9) and (0, 4):
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{4-9}{0-(-4)}=-\dfrac{5}{4}[/tex]
The y-intercept is the point at which the graph intersects the y-axis, so the y-value when x = 0. From observation of the graph, the line crosses the y-axis at (0, 4), therefore the value of b is b = 4.
Substitute the slope m = -5/4 and the y-intercept b = 4 into the slope-intercept form to create the equation of the line:
[tex]y=-\dfrac{5}{4}x+4[/tex]
