Question

10.
Write an equation in point-slope form for the line through the given point with the given slope.

(9, –1); m = 4/3

Answer 1

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

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

where \((x_1, y_1)\) is a point on the line and \(m\) is the slope.

Given the point \((9, -1)\) and the slope \(m = \frac{4}{3}\), we can substitute these values into the formula:

- \(x_1 = 9\)
- \(y_1 = -1\)
- \(m = \frac{4}{3}\)

Now substituting these into the equation:

\[
y - (-1) = \frac{4}{3}(x - 9)
\]

This simplifies to:

\[
y + 1 = \frac{4}{3}(x - 9)
\]

So the equation in point-slope form is:

\[
y + 1 = \frac{4}{3}(x - 9)
\]