Question

Write an equation of the line that passes through the given points.

(-1,7)and (3,-9)

Answer 1

First, we need to find the slope of the line passing through the given points. The formula for finding the slope, m, given two points (x₁, y₁) and (x₂, y₂) is:

m = (y₂ - y₁)/(x₂ - x₁)

Using the points (-1,7) and (3,-9):

m = (-9 - 7)/(3 - (-1))
m = (-16)/(3 + 1)
m = -16/4
m = -4

Now that we have the slope, we can use the point-slope form of the equation of a line to find the equation. The point-slope form is:

y - y₁ = m(x - x₁)

Using the point (-1,7) and the slope m = -4:

y - 7 = -4(x - (-1))
y - 7 = -4(x + 1)
y - 7 = -4x - 4
y = -4x - 4 + 7
y = -4x + 3

The equation of the line passing through the points (-1,7) and (3,-9) is y = -4x + 3.