(-7,-3) and (-12,5)
What passes through the slope intercept

Find the slope of the line through (x1,y1) = (-7,-3) and (x2,y2) = (-12,5)

m = (y2 - y1)/(x2 - x1)

m = (5 - (-3))/(-12 - (-7))

m = (5 + 3)/(-12 + 7)

m = (8)/(-5)

m = -8/5

Plug m = -8/5 and (x1,y1) = (-7,-3) into the point slope formula. Solve for y.

y - y1 = m(x - x1)

y - (-3) = (-8/5)(x - (-7))

y + 3 = (-8/5)(x + 7)

y + 3 = (-8/5)x + (-8/5)(7) distribute

y + 3 = (-8/5)*x - 56/5 multiply

y + 3 - 3 = (-8/5)*x - 56/5 - 3 ... subtract 3 from both sides

y = (-8/5)*x - 56/5 - 15/5 ... rewrite "3" as "15/5"

y = (-8/5)*x - 71/5 combine like terms

This equation is in slope-intercept form y = mx+b with m = -8/5 = -1.6 as the slope and b = -71/5 = -14.2 as the y intercept.

If you want the equation in standard form (Ax+By = C), then you could follow these steps shown below

y = (-8/5)*x - 71/5

5y = 5((-8/5)*x - 71/5) ... multiply both sides by 5

5y = -8x - 71

5y+8x = -8x - 71+8x ... add 8x to both sides

8x+5y = -71

This is in the form Ax+By = C with A = 8, B = 5, C = -71.

step-by-step explanation: