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)

Question

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