How do you find the slope that is perpendicular to the line #2x+3y=7#?
Rearrange the equation into the form y=mx+c where m is the gradient and c is the y intercept.
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.
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.
See a solution process below:
This equation is in Standard Linear form. The standard form of a linear equation is:
Where, if at all possible,
The slope of an equation in standard form is:
Let's call the slope of a perpendicular line:
The formula for this slope is the inverse negative of the slope of the other line, or: