Question

Which of the following are point-slope equations of the line going through (-3, 4) and (2, 1)? Check all that apply.

Answer 1

first find the slope using slope formula : slope (m) = (y2 - y1) / (x2 - x1)
(-3,4) x1 = -3 and y1 = 4
(2,1) x2 = 2 and y2 = 1
now we sub
slope(m) = (1 - 4) / (2 - (-3)
slope(m) = -3/(2 + 3)
slope(m) = -3/5

now we will use point slope form on both sets of points :
point slope formula is : y - y1 = m(x - x1)
(-3,4) -- x1 = -3 and y1 = 4
slope(m) = -3/5
now we sub
y - 4 = -3/5(x - (-3)
y - 4 = -3/5(x + 3)====> here is one

(2,1) x1 = 2 and y1 = 1
slope(m) = -3/5
y - y1 = m(x - x1)
now we sub
y - 1 = -3/5(x - 2) ====> here is the other one

your 2 point slope equations are :
y - 4 = -3/5(x + 3)
y - 1 = -3/5(x - 2)