Question

A line that includes the point (
–
2,6) has a slope of
–
4. What is its equation in point-slope form?
Use the specified point in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
y–
=
x–

Answer 1

To write the equation of a line in point-slope form, you can use the formula:

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

where \(m\) is the slope, and \((x_1, y_1)\) is a point on the line.

Given the point \((-2, 6)\) and the slope \(m = -4\), you can substitute these values into the formula:

1. \(x_1 = -2\)
2. \(y_1 = 6\)
3. \(m = -4\)

Now plug these values into the point-slope form:

\[
y - 6 = -4(x - (-2))
\]

This simplifies to:

\[
y - 6 = -4(x + 2)
\]

You can rewrite the equation in point-slope form as:

\[
y - 6 = -4(x + 2)
\]

So, the final answer is:

\[
y - 6 = -4(x + 2)
\]