Write an equation in point-slope form for the line that passes through the given points.(4,−6), (6,−4)4,-6, 6,-4

The point-slope form of a line is given by the equation:

y - y1 = m(x - x1)

where m is the slope of the line and (x1, y1) is a point on the line.

Step 1: Calculate the slope (m) of the line using the formula:

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

Here, (x1, y1) = (4, -6) and (x2, y2) = (6, -4).

So, m = (-4 - (-6)) / (6 - 4) = 2 / 2 = 1

Step 2: Substitute m = 1, x1 = 4 and y1 = -6 into the point-slope form equation:

y - (-6) = 1(x - 4)

Simplify to get the final equation:

y + 6 = x - 4

or

y = x - 10

This is the equation of the line in point-slope form that passes through the points (4, -6) and (6, -4).