How do you write an equation in the point slope form of the line that passes through the given points 1 8 4 6?

To write the equation of a line in point-slope form, we first need to determine the slope of the line that passes through the two points. The points given are (1, 8) and (4, 6).

The formula to find the slope (m) between two points (x₁, y₁) and (x₂, y₂) is:

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

Substituting the points:

m = (6 - 8) / (4 - 1) = -2 / 3

Now that we have the slope, we can use one of the points and the point-slope formula to write the equation. The point-slope form is given by:

y - y1 = m(x - x1)

Using the point (1, 8) and our slope (-2/3), we substitute into the formula:

y - 8 = (-2/3)(x - 1)

This is the point-slope form of the equation for the line that passes through the given points. You can also use the other point (4, 6) to verify that you will get the same equation. This form is particularly useful for graphing or determining additional points on the line quickly.