Question

15 points

The line AB←→ passes through the points A(−3,6) and B(5,−2).

Which equations could be for AB←→ in point-slope form?

MULTIPLE CHOICES
y+2=−4(x−5)
y−6=−(x+3)
y=−x+3
y+2=−(x−5)
y−2=−(x−1)
y+2=x−5
y−6=x+3
y−6=−4(x+3)

Answer 1

y - 6 = -(x + 3) and y + 2 = - (x - 5).

The line AB passes through the points A(-3, 6) and B(5, -2). Find the point-slope form.

First, we have to calculate the slope using the equation m = (y₂ - y₁)/(x₂ - x₁):

x, y

A(-3, 6)

B( 5,-2)

m = [-2 - (6)]/[5 - (-3)] = (-2 - 6)/(5 + 3)

m = -8/8

m= -1

Writing the point-slope form equation as (y - y₁) = m (x - x₁), with A(-3, 6):

y - 6 = -1[(x -(-3)]

y - 6 = - (x + 3)

Writing the point-slope form equation as (y - y₁) = m (x - x₁), with B(5, -2):

y - (-2) = - (x - 5)

y + 2 = - (x - 5)