Question

How do you find the slope of the line parallel to and perpendicular to $y=3x-4$ ?

Answer 1

To find the slope of the line parallel to $y=3x-4$ , we have to express the given equation in slope-intercept form. We know that slope-intercept form is given as
$y=mx+c$ , where m is the slope and c is the y-intercept. We know that a line parallel to another line will have the same slopes. A line perpendicular to another line, say, $y=mx+c$ will have a negative of the reciprocal of the slope of $y=mx+c$ . We can denote this as ${{m}_{p}}=-\dfrac{1}{m}$ .

Complete step by step solution:
We have to find the slope of the line parallel to and perpendicular to $y=3x-4$ . First, let us express the given equation in slope-intercept form. We know that slope-intercept form is given as
$y=mx+c$ , where m is the slope and c is the y-intercept.
Let us compare the above equation with $y=3x-4$ . We can see that $m=3,c=-4$ .
We know that a line parallel to another line will have the same slopes. Hence, the slope of the line parallel to $y=3x-4$ will be 3.
We know that a line perpendicular to another line, say, $y=mx+c$ will have a negative of the reciprocal of the slope of $y=mx+c$ . We can denote this as ${{m}_{p}}=-\dfrac{1}{m}$ .
$\Rightarrow {{m}_{p}}=-\dfrac{1}{3}$

Note: Students have a chance to make mistakes by writing the slopes for parallel line as ${{m}_{p}}=-\dfrac{1}{m}$ and that for perpendicular line as m. They must always convert the given equation into slope-intercept form.