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? (1 point)
Responses

x−2y=−16
x minus 2 y equals negative 16

y=12x+8
y equals Start Fraction 1 over 2 End Fraction x plus 8

−12x+y=8
negative Start Fraction 1 over 2 End Fraction x plus y equals 8

2x−2y=−16

Answer 1

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

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

Here, \((x_1, y_1) = (2, 9)\) and \(m = \frac{1}{2}\). Plugging in these values, we get:

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

Now we can simplify this equation:

\[
y - 9 = \frac{1}{2}x - 1
\]
\[
y = \frac{1}{2}x + 8
\]

Next, we need to convert this equation into standard form \(Ax + By = C\).

Starting from:

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

We can rearrange it to get:

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

To eliminate the fraction, we can multiply the entire equation by 2:

\[
-1x + 2y = 16
\]

This can also be written as:

\[
x - 2y = -16
\]

So, the standard form of the equation is:

\[
x - 2y = -16
\]

Thus, the correct response from the given options is:

**x − 2y = −16**