Remember that for two equations to be perpendicular, their slopes must be the negative reciprocal of each other.
In the given equation, y = -2x + 18, the slope is -2.
Therefore, the slope of the line perpendicular to this equation must be 1/2.
So, now we have slope = 1/2 and a point at (-4, 12).
Let's determine the equation using the slope-point formula.
[tex]y-y_1=m(x-x_1)[/tex]
where m = slope and (x₁, y₁) = the coordinate of the given point.
Let's replace the variables in the formula with their corresponding numerical values. m = 1/2, x₁ = -4, y₁ = 12
[tex]y-12=\frac{1}{2}(x-(-4))[/tex]
Then, simplify.
[tex]y-12=\frac{1}{2}(x+4)[/tex]
Multiply 1/2 by the terms inside the parenthesis.
[tex]y-12=\frac{1}{2}x+2[/tex]
Add 12 on both sides of the equation.
[tex]y-12+12=\frac{1}{2}x+2+12[/tex][tex]y=\frac{1}{2}x+14[/tex]
Hence, the equation of the line perpendicular to y = -2x + 18 and passes through the point (-4, 12) is y = 1/2x + 14 as shown above.
See the graph below:
