Question

What is the slope of the line that is perpendicular to the graph of y=-2/3x+2

Answer 1

• 3/2

Solution:

Hi! Perpendicular lines have slopes that are opposite reciprocals of each other.

The opposite reciprocal of -2/3 is 3/2. See, we changed the sign from negative to positive, and switched the order of the numerator and the denominator.

We come to the conclusion that the slope of the line which is perpendicular to y=-2/3x+2 is 3/2.

Problem solved! It's been a pleasure helping you.

Answer 2

Slope-Intercept form of the equation of a line is the following:

`y=mx+b`

Where "m" is the slope of the line and "b" is the y-intercept.

In this case you have this equation of the line written in Slope-Intercept form:

`y=-(2)/(3)x+2`

So you can identify that the slope and the y-intercept are the shown below:

`\begin{gathered} m_1=-(2)/(3) \\ b=2 \end{gathered}`

When two lines are perpendicular, their slopes are opposite reciprocal. Knowing that in this case both lines are perpendicular and knowing the slope of one of them, you can determine that the slope of the other line is:

`m_2=(3)/(2)`