Perpendicular lines intersect to form a 90° angle. They form a sort of X-shape.
The slope of a line perpendicular to another line is the negative reciprocal, that is,
.
For your equation, the slope is –7. That means the slope of its perpendicular line must be
.
Now, we must also find such a line that passes through (7, 5). It is easiest to write this in point-slope form,
.
We get
. Technically, we are done, but it is customary to convert this into slope-intercept form,
.
.
And that's our final answer. We can verify the solution graphically. See attached.
In general, our steps are:
<span><span>1) Find the slope of the given line if it is not given directly.
</span><span>2) Find the slope of the perpendicular line (the negative reciprocal).
</span>3) Identify the point it must pass through.
<span>4) Substitute the values into the point-slope form.
</span><span>5) Write the equation in slope-intercept form.</span></span>