Question

A line passes through the point (4,
–
2) and has a slope of
1
2
. Which shows an equation for this line written in standard form?

Answer 1

To find the equation of the line that passes through the point (4, -2) with a slope of \( \frac{1}{2} \), we can start with the point-slope form of the equation of a line:

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

Where \( (x_1, y_1) \) is the point (4, -2) and \( m \) is the slope \( \frac{1}{2} \).

Substituting the values into the point-slope formula:

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

This simplifies to:

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

To eliminate the fraction, we can multiply both sides by 2:

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

Expanding the left side:

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

Now, we rearrange to get it in standard form \( Ax + By = C \):

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

\[
-x + 2y = -8
\]

Multiplying through by -1 to keep the \( x \) term positive (if desired):

\[
x - 2y = 8
\]

Thus, the equation in standard form is:

\[
x - 2y = 8
\]