How do you find the slope that is perpendicular to the line #4x+5y= -5#?
Let's start with the original equation:
From here, we can manipulate the equation into the slope-intercept form. We first move the
Next, we divide both sides by
We then simplify the right portion of the equation:
And further simplification follows:
We then rearrange the entire equation to clearly show the equation in slope-intercept form:
Now that we have the equation in slope-intercept form, we can clearly see that
From here, it is easy. The product of a slope and its perpendicular slope is always
If we set
Then, we can isolate
Thus, the slope of the line perpendicular to the line
The slope perpendicular to a line is the opposite reciprocal of the slope of the given line.
For example, if the slope of a line is 2, the slope of a line perpendicular to the line with slope 2 must be
Because in your case the line is in standard form (i.e.
You can also find the slope,
The slope of a line perpendicular to this line must be the opposite reciprocal, so