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.