Question

A) 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? (1 point)

Answer 1

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

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

Where:
- \( m \) is the slope,
- \( (x_1, y_1) \) is a point on the line.

Given:
- Slope \( m = -\frac{1}{2} \)
- Point \( (x_1, y_1) = (4, 6) \)

Substituting these values into the point-slope formula gives:

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

Now, we will simplify this equation:

1. Distribute the slope on the right-hand side:

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

2. Add 6 to both sides:

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

Now we need to convert this to standard form, which is:

\[
Ax + By = C
\]

Where \( A \), \( B \), and \( C \) are integers, and \( A \) is non-negative.

To get the equation in standard form, we can rearrange:

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

Now, to eliminate the fraction, multiply the entire equation by 2:

\[
x + 2y = 16
\]

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

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