Question

Which is an equation in point-slope form for the given point and slope? Point:(2,-6) Slope:-3/4

Answer 1

The equation for point-slope form is 

$y-y_{1}=m(x-x_{1})$

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):

$y-(-6)=- \frac{3}{4}(x-2) \\ or \\ y+6=- \frac{3}{4}(x-2)$

If you're looking for slope-intercept form you can simplify the equation:

$y+6=- \frac{3}{4}(x-2) \\ \\ y+6=- \frac{3}{4}x+ \frac{6}{4} \\ \\ y+6-6=- \frac{3}{4}x+ \frac{6}{4}-6 \\ \\ y=- \frac{3}{4}x- \frac{18}{4}$

If you're looking for the standard form of the equation, you can take the slope-intercept equation and turn it into standard form:

$y=- \frac{3}{4}x- \frac{18}{4} \\ 4y=4(- \frac{3}{4}x- \frac{18}{4}) \\ 4y=-3x-18 \\ 4y+3x=-3x-18+3x \\ 4y+3x=-18 \\ 3x+4y=-18$