Answer :
The equation for point-slope form is
[tex]y-y_{1}=m(x-x_{1})[/tex]
m being the slope, y1 being the second point in the (2, -6) and the x1 being the first point in the (2, -6).
So the equation would look like this (for point-slope):
[tex]y-(-6)=- \frac{3}{4}(x-2) \\ or \\ y+6=- \frac{3}{4}(x-2) [/tex]
If you're looking for slope-intercept form you can simplify the equation:
[tex]y+6=- \frac{3}{4}(x-2) \\ \\ y+6=- \frac{3}{4}x+ \frac{6}{4} \\ \\ y+6-6=- \frac{3}{4}x+ \frac{6}{4}-6 \\ \\ y=- \frac{3}{4}x- \frac{18}{4}[/tex]
If you're looking for the standard form of the equation, you can take the slope-intercept equation and turn it into standard form:
[tex]y=- \frac{3}{4}x- \frac{18}{4} \\ 4y=4(- \frac{3}{4}x- \frac{18}{4}) \\ 4y=-3x-18 \\ 4y+3x=-3x-18+3x \\ 4y+3x=-18 \\ 3x+4y=-18[/tex]
[tex]y-y_{1}=m(x-x_{1})[/tex]
m being the slope, y1 being the second point in the (2, -6) and the x1 being the first point in the (2, -6).
So the equation would look like this (for point-slope):
[tex]y-(-6)=- \frac{3}{4}(x-2) \\ or \\ y+6=- \frac{3}{4}(x-2) [/tex]
If you're looking for slope-intercept form you can simplify the equation:
[tex]y+6=- \frac{3}{4}(x-2) \\ \\ y+6=- \frac{3}{4}x+ \frac{6}{4} \\ \\ y+6-6=- \frac{3}{4}x+ \frac{6}{4}-6 \\ \\ y=- \frac{3}{4}x- \frac{18}{4}[/tex]
If you're looking for the standard form of the equation, you can take the slope-intercept equation and turn it into standard form:
[tex]y=- \frac{3}{4}x- \frac{18}{4} \\ 4y=4(- \frac{3}{4}x- \frac{18}{4}) \\ 4y=-3x-18 \\ 4y+3x=-3x-18+3x \\ 4y+3x=-18 \\ 3x+4y=-18[/tex]
