Question

Through (-4,3) , perpendicular to m=-2/3​

Answer 1

Answer:

The equation of the line:

$y=\frac{3}{2}x+9$

Step-by-step explanation:

Given

• The point (-4, 3)

• m = -2/3

We know that a line perpendicular to another line contains a slope that is the negative reciprocal of the slope of the other line, such as:

slope = m = -2/3

perpendicular to m = -1/m

                                 $=-\frac{1}{\left(\frac{-2}{3}\right)}=\frac{3}{2}$

Using the point-slope form of the line equation

$y-y_1=m\left(x-x_1\right)$

substituting the values m = 3/2 and the point (-4, 3)

$y-3=\frac{3}{2}\left(x-\left(-4\right)\right)$

$y-3=\frac{3}{2}\left(x+4\right)$

Add 3 to both sides

$y-3+3=\frac{3}{2}\left(x+4\right)+3$

$y=\frac{3}{2}x+9$

Thus, the equation of the line:

$y=\frac{3}{2}x+9$