find the equation of the line that passes through (-1,-2)(4,-5)

Start by finding the slope, which can be determined by the

numbers given.

P1 (x1, y1) (-1, -2)

P2 (x2, y2) (4, -5)

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

m = (-5 - (-2)) / (4 - (-1))

m = (-5 + 2) / (4 + 1)

m = -3 / 5

We now have enough information to find the y-intercept, b.

y = mx + b

y - mx = b

We'll use P2 for this.

b = -5 - ((-3/5) * 4)

b = -5 - (-12/5) = -5 + (12/5)

Here, we will change the -5 into a fraction.

b = (-25/5) + 12/5) = -13/5

With the slope and the intercept known, we write the general equation:

y = (-3/5)x - 13/5

Test them with P1. We know x1 = -1; find y1.

y = (-3/5)(-1) - 13/5

y = 3/5 - 13/5 = -10/5 = -2

Verified.