The inverse is found when we swap the x,y variables of the function of the original line:
⇒ let's find the equation of the original line
⇒ (slope-intercept form), we need the slope, and the y-intercept
- slope = [tex]\frac{y2-y1}{x2-x1}=\frac{0--4}{9-0} =\frac{4}{9}[/tex]
- y-intercept ⇒ point where x-coordinate equals zero ⇒ (0,-4)
⇒ equation: [tex]y = \frac{4}{9}x-4[/tex]
Now let's swap the x,y variable's position to find the inverse function
[tex]x=\frac{4}{9}y-4\\ x+4=\frac{4}{9}y\\ 9x+36=4y\\ y=\frac{9}{4}x+9[/tex]
By comparing all these graphs:
⇒ Choice (C) is the graph that contains the original graph and the
inverse graph
Hope that helps!
