Respuesta :
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
- so the slope of the line is -2/3.
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]