Give the slope-intercept form of the equation of the line that is perpendicular to 5x + 4y = 4 and contains (-1, 9).

Question

I know the slope intercept form is y=mx+b  I also know that perpendicular lines have negative reciprocals of each other. I just don't know what to do now.

Answer 1

Step1 To find m1

Given line slope say m1

5x+4y = 4

Subtract 5x from each side.

5x-5x+4y = 4-5x

4y = 4-5x

Divide by 4 to each side.

4y/4 = (4-5x)/4

y = 4/4-5x/4

y = 1-(5/4)x

y = (-5/4)x+1

Slope m1 = -5/4

Step2  To find m2

Perpendicular line slope say m2

We know that m1*m2 = -1

-5/4*m2 = -1

Multiple by negitive 4/5 to each side.

-5/4*-4/5m2 = -1*-4/5

m2 = 4/5

Step3 To find final line equation

Equation to the perpendicular line which is passes through(-1,9) is y-y1 =m2(x-x1)

y-9 = 4/5(x-(-1))

y-9 = 4/5(x+1)

Cross multiply

5(y-9) = 4(x+1)

5y-45 = 4x+4

5y = 4x+4+45

5y =4x+49

Divide by 5 to each side.

5y/5 = (4x+49)/5

y = (4/5)x+49/5