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)
x+
y=

Answer 1

To find the equation of a line in standard form \(Ax + By = C\), we can start with the point-slope form of a line, which is given by:

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

where \(m\) is the slope, and \((x_1, y_1)\) is a point on the line. Here, the slope \(m = -12\) and the point given is \((4, 6)\).

Substituting the values into the point-slope form:

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

Now, simplify and rearrange to get the equation in standard form.

1. Distributing \(-12\):

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

2. Adding 6 to both sides:

\[
y = -12x + 54
\]

3. Rearranging to get standard form by moving all terms to one side:

\[
12x + y = 54
\]

Thus, the equation in standard form is:

\[
12x + y = 54
\]

So, the answer is:

\[
A = 12, \quad B = 1, \quad C = 54
\]

In the form \(x + y = C\), we have to rearrange it:

Divide the entire equation \(12x + y = 54\) by \(12\) if needed, to put it in \(x + y = C\):

\[
x + \frac{y}{12} = \frac{54}{12}
\]

However, if you want to keep it in the standard form:

\[
12x + y = 54
\]

That's the standard form solution you need!