Question

A line with a slope of m=−1/2 passes through the point (4,6). What is the equation of the line in standard form?

Answer 1

To find the equation of a line given a slope and a point, we can use the point-slope form of the equation of a line:

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

where \(m\) is the slope, and \((x_1, y_1)\) is the given point. Here, the slope \(m = -\frac{1}{2}\) and the point is \((4, 6)\).

Plugging in the values, we have:

\[
y - 6 = -\frac{1}{2}(x - 4)
\]

Next, we simplify the equation:

1. Distribute the slope on the right side:

\[
y - 6 = -\frac{1}{2}x + 2
\]

2. Add 6 to both sides:

\[
y = -\frac{1}{2}x + 8
\]

Now we have the equation in slope-intercept form (\(y = mx + b\)). To convert it to standard form \(Ax + By = C\), we rearrange the terms:

1. Add \(\frac{1}{2}x\) to both sides:

\[
\frac{1}{2}x + y = 8
\]

2. To eliminate the fraction, multiply the entire equation by 2:

\[
x + 2y = 16
\]

Now we have the equation in standard form. The final answer is:

\[
\boxed{x + 2y = 16}
\]