How do you find the slope that is perpendicular to the line #4x+5y= -5#?
The slope of the line perpendicular to the line
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 that is 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