What is the equation in point-slope form for a line that passes through the points (-6, 38) and (2, -22)?

1 answer

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, we use the formula:

m = (y₂ - y₁) / (x₂ - x₁)

Given the points (-6, 38) and (2, -22), we can plug in the values:

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

Now that we have the slope, we can choose one of the given points, such as (-6, 38), and plug it into the point-slope form equation:

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

Then, we simplify the equation:

y - 38 = -7.5x - 45
y = -7.5x - 45 + 38
y = -7.5x - 7

Therefore, the equation in point-slope form for a line that passes through the points (-6, 38) and (2, -22) is y = -7.5x - 7.