Question

Find point slope form (2,15) and (6,9)

Answer 1

To find the point-slope form of a line that passes through the points \((2, 15)\) and \((6, 9)\), we first need to calculate the slope \(m\) of the line using the formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Let's identify the points:
- \((x_1, y_1) = (2, 15)\)
- \((x_2, y_2) = (6, 9)\)

Substituting the values in:

\[
m = \frac{9 - 15}{6 - 2} = \frac{-6}{4} = -\frac{3}{2}
\]

Now that we have the slope \(m = -\frac{3}{2}\), we can use the point-slope form of the equation of a line, which is given by:

\[
y - y_1 = m(x - x_1)
\]

We can use either of the two points. Let's use the point \((2, 15)\):

\[
y - 15 = -\frac{3}{2}(x - 2)
\]

This is the point-slope form of the line that passes through the points \((2, 15)\) and \((6, 9)\). If you’d like to express it with the other point, just replace \((2,15)\) with \((6,9)\) in the equation, and you will get an equivalent equation.