Answer:
The slope-intercept equation is:
[tex]y=\frac{3}{2}x+1[/tex]
Step-by-step explanation:
Given the equation
[tex]y-4=-\frac{2}{3}\left(x-6\right)[/tex]
comparing it with the point-slope form of the line equation
[tex]y-y_1=m\left(x-x_1\right)[/tex]
where m is the slope
As we know that the slope of the perpendicular line is basically the negative reciprocal of the slope of the line, so
The slope of the perpendicular line will be: 3/2
The point-slope form of the equation of the perpendicular line that goes through (-2, -2) is:
[tex]y-y_1=m\left(x-x_1\right)[/tex]
[tex]y-\left(-2\right)=\frac{3}{2}\left(x-\left(-2\right)\right)[/tex]
[tex]y+2=\frac{3}{2}\left(x+2\right)[/tex]
writing the line equation in the slope-intercept form
[tex]y+2=\frac{3}{2}\left(x+2\right)[/tex]
subtract 2 from both sides
[tex]y+2-2=\frac{3}{2}\left(x+2\right)-2[/tex]
[tex]y=\frac{3}{2}x+1[/tex]
Thus, the slope-intercept equation is:
[tex]y=\frac{3}{2}x+1[/tex]
Here,
As the slope-intercept form is
[tex]y=mx+b[/tex]
where m is the slope and b is the y-intercept
so
[tex]y=\frac{3}{2}x+1[/tex]
m=3/2
b = y-intercept = 1
Therefore, the slope-intercept equation is:
[tex]y=\frac{3}{2}x+1[/tex]
