Question

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

2x – y = –4
2x – y = 4
y = 2x – 4
y equals StartFraction one-half EndFraction x minus 4.

Answer 1

To find the equation of the line that passes through the points (0, -4) and (2, 0), we can first find the slope (m) of the line using the formula:

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

Using the points (0, -4) as \((x_1, y_1)\) and (2, 0) as \((x_2, y_2)\):

\[
m = \frac{0 - (-4)}{2 - 0} = \frac{0 + 4}{2} = \frac{4}{2} = 2
\]

Now that we have the slope \(m = 2\), we can use the point-slope form of the equation of a line, which is:

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

Using point (0, -4):

\[
y - (-4) = 2(x - 0)
\]
\[
y + 4 = 2x
\]
\[
y = 2x - 4
\]

Next, we convert \(y = 2x - 4\) into standard form \(Ax + By = C\).

Starting with:

\[
y = 2x - 4
\]

Rearranging it gives:

\[
-2x + y = -4
\]

To write it in the standard form \(Ax + By = C\) where A, B, and C are all integers, we can multiply through by -1 to make A positive:

\[
2x - y = 4
\]

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

\[
\boxed{2x - y = 4}
\]