Answer:
The equation of graphed function is [tex]y=\frac{3}{2}x-3[/tex].
Step-by-step explanation:
From the given graph it is clear that the x-intercept of the line is 2 and y-intercept of the line is -3. It means the line passing through the points (2,0) and (0,-3).
If a line passing through two point, then the slope of the function is
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
The slope of the line is
[tex]m=\frac{-3-0}{0-2}=\frac{-3}{-2}=\frac{3}{2}[/tex]
The slope intercept form of a line is
[tex]y=mx+b[/tex]
where, m is slope and b is y-intercept.
Since the slope of the line is [tex]\frac{3}{2}[/tex] and y-intercept is -3, therefore the equation of the function is
[tex]y=\frac{3}{2}x+(-3)[/tex]
[tex]y=\frac{3}{2}x-3[/tex]
Thus, the equation of graphed function is [tex]y=\frac{3}{2}x-3[/tex].
