Question

Write the equation that is parallel to y=-x+8 and goes through (-2,4)

a
y=-x+2

b
y=x+2

c
y=-x-5

d
y=-x+10

Answer 1

To find the equation of a line that is parallel to \( y = -x + 8 \) and passes through the point \((-2, 4)\), we first note that parallel lines have the same slope. The slope of \( y = -x + 8 \) is \(-1\). Therefore, the line we are looking for will also have a slope of \(-1\).

Next, we can use the point-slope form of the equation of a line, which is given by:

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

where \( (x_1, y_1) \) is a point on the line, and \( m \) is the slope. Plugging in our slope and the point \((-2, 4)\):

\[
y - 4 = -1(x - (-2))
\]

Simplifying this:

\[
y - 4 = -1(x + 2)
\]
\[
y - 4 = -x - 2
\]
\[
y = -x - 2 + 4
\]
\[
y = -x + 2
\]

Thus, the equation of the line we want is:

\[
y = -x + 2
\]

Looking at the answer choices, the correct answer is:

**a. \( y = -x + 2 \)**.