Question

A line passes through the point (2,9) and has a slope of 1/2 which option correctly writes the equation of the line in standard form

Answer 1

To write the equation of the line in standard form, we start with the point-slope form of the line equation:

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

Where \((x_1, y_1)\) is the point on the line and \(m\) is the slope. For your line:

- The point \((x_1, y_1)\) is \((2, 9)\)
- The slope \(m\) is \(\frac{1}{2}\)

Substituting these values into the point-slope form:

\[
y - 9 = \frac{1}{2}(x - 2)
\]

Now, we simplify this equation:

\[
y - 9 = \frac{1}{2}x - 1
\]

Next, we'll add 9 to both sides:

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

Now, we'll convert this equation into standard form \(Ax + By = C\). First, multiply every term by 2 to eliminate the fraction:

\[
2y = x + 16
\]

Next, rearrange the equation to the standard form \(Ax + By = C\):

\[
-x + 2y = 16
\]

To express this with a positive \(A\), we can multiply the entire equation by -1:

\[
x - 2y = -16
\]

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

\[
x - 2y = -16
\]