How do you find the slope that is perpendicular to the line #2x+3y=7#?

2 Answers
Jul 8, 2017

Answer:

#3/2#

Explanation:

Rearrange the equation into the form y=mx+c where m is the gradient and c is the y intercept.

#y=-2/3x+7#

The slope that is perpendicular to that line has a gradient with the negative reciprocal i.e. change the sign from minus to plus (or vice versa) and then flip it upside down.

#-2/3# becomes #3/2#

You need a little more information to find the resulting equation i.e. a point which the line goes through where you will reuse the equation above (y=mx+c) to find the new y intercept.

Jul 8, 2017

Answer:

See a solution process below:

Explanation:

This equation is in Standard Linear form. The standard form of a linear equation is: #color(red)(A)x + color(blue)(B)y = color(green)(C)#

Where, if at all possible, #color(red)(A)#, #color(blue)(B)#, and #color(green)(C)#are integers, and A is non-negative, and, A, B, and C have no common factors other than 1

#color(red)(2)x + color(blue)(3)y = color(green)(7)#

The slope of an equation in standard form is: #m = -color(red)(2)/color(blue)(3)#

Let's call the slope of a perpendicular line: #m_p#

The formula for this slope is the inverse negative of the slope of the other line, or:

#m_p = -1/m#

Therefore:

#m_p = -1/(-2/3) = 3/2#