Question

What is the equation in point-slope form of the line passing through (-2,-5) and (2, 3)?

A) (y + 2) = -2(x + 5)
B) (Y - 2) = 2(x – 3)
C) (y - 3) = 2(x - 2)
D) (y + 3) = -2(x + 2)

Answer 1

The equation in point-slope form of the line passing through (-2,-5) and (2,3) is (y + 5) = 2(x + 2).

Step-by-step explanation:

To find the equation in point-slope form of the line passing through the points (-2,-5) and (2,3), we can use the formula:
y - y1 = m(x - x1)

where (x1, y1) and (x, y) are the coordinates of the two points, and m is the slope of the line.

First, let's find the slope:
m = (y2 - y1) / (x2 - x1)
m = (3 - (-5)) / (2 - (-2))
m = 8 / 4
m = 2

Next, we can choose one of the points, let's use (-2,-5), and substitute it into the formula:
y - (-5) = 2(x - (-2))
y + 5 = 2(x + 2)

Simplifying the equation gives:
(y + 5) = 2(x + 2)

So, the equation in point-slope form of the line passing through (-2,-5) and (2,3) is (y + 5) = 2(x + 2).