Question

A) 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? (1 point)

Answer 1

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

\[ y = mx + b \]

where \( m \) is the slope and \( b \) is the y-intercept. Given the slope \( m = \frac{1}{2} \) and the point \( (2, 9) \), we can substitute these values into the equation to find \( b \).

1. Substitute the slope and the coordinates of the point into the equation:
\[
9 = \frac{1}{2}(2) + b
\]

2. Calculate:
\[
9 = 1 + b
\]
\[
b = 9 - 1 = 8
\]

So the equation in slope-intercept form is:
\[
y = \frac{1}{2}x + 8
\]

Next, we need to convert this to standard form, which is generally written as \( Ax + By = C \). To do that, we'll rearrange the equation:

1. Multiply the slope-intercept form by 2 to eliminate the fraction:
\[
2y = x + 16
\]

2. Rearrange it to standard form:
\[
-x + 2y = 16
\]

3. To make the leading coefficient positive (if preferred), we can multiply the entire equation by -1:
\[
x - 2y = -16
\]

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

\[
x - 2y = -16
\]

This is the correct standard form of the equation of the line.