Question

A line passes through the point (4,-2) and has a slope of .5. what is an equation for this line in standard form?
A) 1/2x+y=-6
B) -1/2x+y=6
C)1/2x+y=4
D)-1/2x+y=-4

Answer 1

To find the equation of the line in standard form, we can start with the slope-intercept form of the line, which is given by the equation:

\[
y = mx + b
\]

where \( m \) is the slope and \( b \) is the y-intercept. Given that the slope \( m = 0.5 \), we can substitute that into the equation:

\[
y = 0.5x + b
\]

Next, we use the point (4, -2) to find \( b \). Substituting \( x = 4 \) and \( y = -2 \):

\[
-2 = 0.5(4) + b
\]

Calculating \( 0.5(4) \):

\[
-2 = 2 + b
\]

Now, solving for \( b \):

\[
b = -2 - 2 = -4
\]

So the equation of the line in slope-intercept form is:

\[
y = 0.5x - 4
\]

To convert this to standard form \( Ax + By = C \), we can rearrange it:

\[
0.5x - y = 4
\]

Next, we can eliminate the decimal by multiplying the entire equation by 2:

\[
2(0.5x) - 2y = 2(4)
\]
\[
x - 2y = 8
\]

This doesn't match any of the given options yet, so let's rewrite in a more standard form. Adding \( 2y \) to both sides gives us:

\[
x + 2y = 8
\]

Now we can rearrange it to match the form that is presented in the options. We can rewrite it as:

\[
-1/2x + y = -4
\]

This matches option D:

\[
D) -\frac{1}{2}x + y = -4
\]

To verify the form matches, if we add \(\frac{1}{2}x\) to both sides:

\[
y = \frac{1}{2}x - 4
\]

Thus, the equation you can choose as the answer which represents the line in standard form is option D) \(-\frac{1}{2}x + y = -4\).

Summarizing, the answer is:

**D) -1/2x+y=-4**