Question

Which of the following equations represents a line that is perpendicular to y=-4x+9 and passes through the point, (4,5)?

Answer 1

Answer:

$y = \frac{1}{4}x + 4 \\or\\4y = x + 16$

Step-by-step explanation:

Given equation of line is:

y = -4x+9

Comparing it with the standard form

y = mx+b

m = -4

As we know that the product of slopes of perpendicular lines is -1

Let m1 be the slope of perpendicular line

m * m1 = -1

-4 * m1 = -1

m1 = -1/-4

m1 = 1/4

In order to find the value of b, putting the point in standard form

5 = (1/4)*4 + b

5 = 1 + b

b = 5-1

b = 4

Putting the value of b and m1 in standard form

$y = \frac{1}{4}x + 4 \\or\\4y = x + 16$ ..