Question

A line passes through the point (2,9) and has a slope of 12. 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 a line in standard form that passes through the point (2, 9) with a slope of 12, we can start by using the point-slope form of the equation of a line:

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

where \( (x_1, y_1) \) is the point (2, 9) and \( m \) is the slope (12):

\[ y - 9 = 12(x - 2) \]

Now, we'll simplify this equation:

1. Distribute the slope:
\[ y - 9 = 12x - 24 \]

2. Add 9 to both sides:
\[ y = 12x - 15 \]

Now we need to convert this equation into standard form, which is generally in the form \( Ax + By = C \).

Starting from:

\[ y = 12x - 15 \]

we can rearrange it:

1. Subtract \( 12x \) from both sides:
\[ -12x + y = -15 \]

2. Multiply through by -1 to get the standard form:
\[ 12x - y = 15 \]

This can also be rewritten as:
\[ 12x - y = 15 \]

To compare it with the given options, let's rewrite it for clarity:

\[ -12x + y = -15 \]

Now, we'll check the options one by one:

1. **x − 2y = −16** (This does not match.)

2. **y = 12x + 8** (This is not equivalent.)

3. **−12x + y = 8** (This does not match.)

4. **2x − 2y = −16** (Dividing the whole equation by 2 gives: \( x - y = -8 \) which does not match.)

After careful comparison, it seems none of the options align with the line's correct equation in standard form.

However, if \( 12x - y = 15 \) is rewritten in a more standard format, it doesn't match.

None of the given responses accurately reflect the equation derived.

The correct response should be something like:
\[ 12x - y = 15 \]
or equivalent forms.

Please double-check choices provided; as of now, none match the derived line equation.