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Use point-slope form to write the equation of a line that passes through the point left parenthesis, minus, 11, comma, minus, 13, right parenthesis(−11,−13) with slope minus, start fraction, 2, divided by, 3, end fraction−
3
2
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Answer 1

To write the equation of a line in point-slope form, we 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.

For this problem:
- The point is \((-11, -13)\), so we have \(x_1 = -11\) and \(y_1 = -13\).
- The slope \(m\) is \(-\frac{2}{3}\).

Now we can substitute these values into the point-slope formula:

\[
y - (-13) = -\frac{2}{3}(x - (-11))
\]

This simplifies to:

\[
y + 13 = -\frac{2}{3}(x + 11)
\]

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

\[
y + 13 = -\frac{2}{3}(x + 11)
\]