Question

2.
Write an equation in point-slope form for the line through the given point with the given slope.

(–3, –7); m = -6/5

Answer 1

To write the equation of a line in point-slope form, you use 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. In this case, the point is \((-3, -7)\) and the slope \(m = -\frac{6}{5}\).

Plugging in the values:

- \(x_1 = -3\)
- \(y_1 = -7\)
- \(m = -\frac{6}{5}\)

The equation becomes:

\[
y - (-7) = -\frac{6}{5}(x - (-3))
\]

This simplifies to:

\[
y + 7 = -\frac{6}{5}(x + 3)
\]

So the equation of the line in point-slope form is:

\[
y + 7 = -\frac{6}{5}(x + 3)
\]