Question

Which is the equation of a line that has a slope of Negative two-thirds and passes through point
(–3, –1)?
y = negative two-thirds x + 1
y = negative two-thirds x + 3
y = negative two-thirds x minus 1
y = negative two-thirds x minus 3

Answer 1

To find the equation of the line with a slope of \(-\frac{2}{3}\) that passes through the point \((-3, -1)\), we can use the point-slope form of the equation of a line, which is:

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

where \((x_1, y_1)\) is the point the line passes through and \(m\) is the slope.

Given:
- Slope \(m = -\frac{2}{3}\)
- Point \((x_1, y_1) = (-3, -1)\)

Substituting the values into the point-slope formula:

\[
y - (-1) = -\frac{2}{3}(x - (-3))
\]

This simplifies to:

\[
y + 1 = -\frac{2}{3}(x + 3)
\]

Now, distributing \(-\frac{2}{3}\):

\[
y + 1 = -\frac{2}{3}x - 2
\]

Next, we subtract \(1\) from both sides to solve for \(y\):

\[
y = -\frac{2}{3}x - 2 - 1
\]

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

Thus, the equation of the line is:

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

Among the provided choices, the correct option is:

**y = negative two-thirds x minus 3**.