Question

A line has this equation: -5y = 4x+40

Write an equation for the perpendicular line that goes through (8,5).

Answer 1

The equation of the second line is;

y = 4x - 27

Explanation:

Firstly, we need the slope of the first line

To get the slope, we need the equation in the general form of ;

y = mx + c

where m is the slope of the line

Thus, we have in this case, to divide through by -5

That will give the slope value as -5/20 = -1/4

If two lines are perpendicular, the product of their slopes is -1

The slope of the line we want to calculate, let us call it m

m * -1/4 = -1

-m = -4

m = 4

So we want to write the equation of a line with slope 4 and point (8,5)

We proceed to use the point-slope form

That will be;

y-y1 = m(x-x1)

y-5 = 4(x-8)

y-5 = 4x-32

y = 4x -32 + 5

y = 4x -27