Answer:
y= -3/2x + 1
Step-by-step explanation:
The slope of this line is 2/3. The slope of the line perpendicular to this line will be the negative reciprocal or -3/2.
Write the equation using the slope m=-3/2 and the point slope form.
[tex]y-y_1=m(x-x_1)\\y--2=-\frac{3}{2}(x-4)\\y+2=-\frac{3}{2}(x-4)[/tex]
This is the equation of the line. You can convert it to slope intercept form:
[tex]y+2=-\frac{3}{2}(x-4)\\y+2 = -\frac{3}{2}x + 3\\y=-\frac{3}{2}x +1[/tex]
