Question

Which equation represents the graph?

a graph of a line that passes through the points 0 comma negative 3 and 3 comma negative 1
y equals negative three halves times x plus 5
y equals negative two thirds times x plus 3
y equals two thirds times x minus 3
y equals three halves times x minus 5

Answer 1

To find the equation of the line that passes through the points (0, -3) and (3, -1), we first need to determine the slope of the line using the slope formula:

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

Using the points (0, -3) as \((x_1, y_1)\) and (3, -1) as \((x_2, y_2)\):

\[
m = \frac{-1 - (-3)}{3 - 0} = \frac{-1 + 3}{3} = \frac{2}{3}
\]

Next, we use point-slope form to find the equation of the line. Point-slope form is given by:

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

Let's use the point (0, -3):

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

This simplifies to:

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

Subtracting 3 from both sides gives:

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

Now, we can see that this matches the equation \(y = \frac{2}{3}x - 3\).

Therefore, the equation that represents the graph is:

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