Question

What is the equation in point-slope form for a line that passes through the points (-6, 38) and

(2, -22)?

Answer 1

The point-slope form of a linear equation is given by y - y1 = m(x - x1), where (x1, y1) are the coordinates of a point on the line and m is the slope of the line.

To find the slope (m), we can use the formula:

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

Using the points (-6, 38) and (2, -22), we have:

m = (-22 - 38) / (2 - (-6))
= (-22 - 38) / (2 + 6)
= (-60) / 8
= -7.5

Now, we can plug in one of the points and the slope into the point-slope form equation:

Let's use the point (-6, 38):

y - y1 = m(x - x1)
y - 38 = -7.5(x + 6)

Thus, the equation in point-slope form for the line passing through the points (-6, 38) and (2, -22) is:

y - 38 = -7.5(x + 6)