Question

A line with a slope of m=−12
 passes through the point (4,6)
. What is the equation of the line in standard form?(1 point)

Answer 1

To find the equation of a line in standard form given the slope \( m = -12 \) and the point \( (4, 6) \), we can use the point-slope form of the line equation, which is given by:

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

Here, \( (x_1, y_1) \) is the point on the line, which is \( (4, 6) \). Substituting the slope and the point into the equation gives us:

\[
y - 6 = -12(x - 4)
\]

Now, we can simplify and rearrange this equation into standard form \( Ax + By = C \).

1. Distribute the slope on the right side:

\[
y - 6 = -12x + 48
\]

2. Add 6 to both sides:

\[
y = -12x + 54
\]

3. Rearrange to get it in the standard form \( Ax + By = C \):

\[
12x + y = 54
\]

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

\[
12x + y = 54
\]