Question

A coordinate plane with a line passing through (negative 3, 0), (0, negative 2) and (3, negative 4).
What is the equation of the graphed line written in standard form?

2x + 3y = –6
2x + 3y = 6
y equals negative StartFraction 2 Over 3 EndFraction x minus 2.
y equals StartFraction 2 Over 3 EndFraction x minus 2.

Answer 1

To find the equation of the line that passes through the points \((-3, 0)\), \((0, -2)\), and \((3, -4)\), we can start by finding the slope (m) of the line using the coordinates of two of the points.

We can use points \((0, -2)\) and \((-3, 0)\) to calculate the slope. The formula for the slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

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

Using \((0, -2)\) as \((x_1, y_1)\) and \((-3, 0)\) as \((x_2, y_2)\):

\[
m = \frac{-2 - 0}{0 - (-3)} = \frac{-2}{3}
\]

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

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

Using point \((0, -2)\):

\[
y - (-2) = -\frac{2}{3}(x - 0)
\]

Simplifying this gives:

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

Now, we can convert this equation into standard form \(Ax + By = C\).

Starting with:

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

Multiply through by 3 to eliminate the fraction:

\[
3y = -2x - 6
\]

Rearranging gives:

\[
2x + 3y = -6
\]

Thus, the equation of the line in standard form is:

\[
2x + 3y = -6
\]

So the correct answer is:

**2x + 3y = –6**