How do you find the line that is perpendicular to y=2/3x+1 and passes through (0, 5)?

2 Answers
Nov 10, 2016

y=-3/2x+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, (rise)/(run, 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

y-y_1=m(x-x_1)

m=-3/2

y_1=5

x_1=0

y-5=-3/2(x-0)

Distribute the -3/2 throughout the set of parenthesis

y-5=-3/2x+0

Add 5 on both sides of the equation

y=-3/2x+5

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

Nov 10, 2016

y = -3/2x+5

Explanation:

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

If m_1 = 2/3," " m_2 = -3/2

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' rarr c = 5

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

y = -3/2x+5