Find the equation of a line that passes through the points; (-6,-4) and (3,8)

Question

I need an equation with these to cordinates

Answer 1

set the slopes equal, "rise over run" difference in y coordinates divided by difference in x coordinates. for the right side use either point

(8+4)/(3+6) = (y-8)/(x-3)

12/9 = 4/3 = (y-8)/(x-3)

y-8 = (4/3)(x-3)

y = (4/3)x - 4 +8

y = (4/3)x +4 is the equation through the two given points, in slope intercept form

or remove the fractions

3y = 4x + 12

4x -3y +12 = 0 in general form

it might help to plot the 2 points and draw a line through them. check to see if the intercept (0,4) is on that line.

or check the answer by plugging in each point into the equation.