Question

through: (-4,5), slope =-2

Answer 1

To find the equation of a line that passes through the point \((-4, 5)\) with a slope of \(-2\), we can use the point-slope form of the equation of a line, which is given by:

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

Here, \(m\) is the slope, and \((x_1, y_1)\) is the point through which the line passes. Substituting in the values:

- \(m = -2\)
- \(x_1 = -4\)
- \(y_1 = 5\)

We can plug in these values:

\[
y - 5 = -2(x - (-4))
\]

This simplifies to:

\[
y - 5 = -2(x + 4)
\]

Now, distribute the \(-2\):

\[
y - 5 = -2x - 8
\]

Next, we add \(5\) to both sides to solve for \(y\):

\[
y = -2x - 8 + 5
\]
\[
y = -2x - 3
\]

Thus, the equation of the line in slope-intercept form is:

\[
y = -2x - 3
\]