How do you find the line that is perpendicular to y=23x+1 and passes through (0, 5)?

2 Answers
Nov 10, 2016

y=32x+5

Explanation:

Perpendicular lines have opposite reciprocal slope, m, in an equation. Meaning, if the slope of a line is a positive fraction, its reciprocal slope would be negative.

The given equation is a linear equation, y=mx+b

Where m is the slope, riserun, and b is the y intercept

To find a line that is perpendicular to the given equation, use the opposite reciprocal slope and point and solve using the point-slope formula

yy1=m(xx1)

m=32

y1=5

x1=0

y5=32(x0)

Distribute the 32 throughout the set of parenthesis

y5=32x+0

Add 5 on both sides of the equation

y=32x+5

And now you can see the slope is the opposite reciprocal of the original equation

Nov 10, 2016

y=32x+5

Explanation:

If lines are perpendicular, one slope is the negative reciprocal of the other.
(Their product is -1)

If m1=23, m2=32

So we have the slope of the line perpendicular to the one given.

The point (0,5) is the y-intercept because the x-value is 0.
This is also known as 'c' c=5

The equation of a line is y=mx+c.
We have mandc

y=32x+5