Answer:
Point of Intersection: (-4, -4)
Step-by-step explanation:
Given the linear equation, y = 3x + 8:
We must determine its inverse, which will enable us to find the point of intersection between the given equation and its inverse.
Start by switching x and y in the given linear equation:
y = 3x + 8
x = 3y + 8
Next, subtract 8 from both sides:
x - 8 = 3y + 8 - 8
x - 8 = 3y
Multiply both sides with ⅓ to isolate y:
⅓ (x - 8) = (3y) ⅓
[tex]\displaytext\mathsf{\frac{1}{3}x\:-\frac{8}{3}\:=\:y}[/tex]
Replace y with [tex]\large{\textit{f}\:^{-1}(\textit{x}\:)}[/tex]:
[tex]\displaytext\mathsf{\textit{f}\:^{-1}(\textit{x}\:)\:=\frac{1}{3}x\:-\frac{8}{3}}[/tex] ⇒ This is the inverse function of y = 3x + 8.
Graph both equations:
Next, we must graph both equations.
Plot the y-intercept, (0, 8), and use the slope of the given linear equation, m = 3, to plot other points on the graph.
Similarly, to graph the inverse function, take the y-intercept, [tex]\displaytext\sf{(0,\:-\frac{8}{3})}[/tex], and use the slope, m = ⅓, to plot other points on the graph.
Attached is the graph of the linear equation, y = 3x + 8, and its inverse, [tex]\displaytext\mathsf{\textit{f}\:^{-1}(\textit{x}\:)\:=\frac{1}{3}x\:-\frac{8}{3}}[/tex] , where it shows that the point of intersection occurs at point, (-4, -4).
