Answer:
The equation of the line is [tex]y = -\frac{3x}{4} - 2[/tex]
Step-by-step explanation:
Equation of a line:
The equation of a line has the following format:
[tex]y = mx + b[/tex]
In which m is the slope and b is the y-intercept.
Perpendicular lines:
When two lines are perpendicular, the multiplication of their slopes is -1.
Perpendicular to the line 4x-3y=18
First, we place this line into the format, to find the slope:
[tex]4x - 3y = 18[/tex]
[tex]3y = 4x - 18[/tex]
[tex]y = \frac{4x}{3} - 6[/tex]
This line has slope 4/3. So, for the perpendicular line, the slope will be of m as such:
[tex]\frac{4m}{3} = -1[/tex]
[tex]4m = -3[/tex]
[tex]m = -\frac{3}{4}[/tex]
So the desired line will have an equation in the following format:
[tex]y = -\frac{3x}{4} + b[/tex]
Passes through the point (8,-8)
We use this to find b. This point means that when [tex]x = 8, y = -8[/tex]. So
[tex]y = -\frac{3x}{4} + b[/tex]
[tex]-8 = -\frac{3*8}{4} + b[/tex]
[tex]-8 = -6 + b[/tex]
[tex]b = -2[/tex]
So
[tex]y = -\frac{3x}{4} - 2[/tex]
