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Question 15 (4 points)

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What is the equation of the line that passes through the points (-4,8) and (1,3)
y=-x+12
y=x+4
y=-x+4
y=x+12

Answer 1

To find the equation of the line that passes through the points \((-4, 8)\) and \((1, 3)\), we first need to find the slope \(m\).

The formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Substituting in the coordinates:

\[
m = \frac{3 - 8}{1 - (-4)} = \frac{-5}{1 + 4} = \frac{-5}{5} = -1
\]

Now that we have the slope \(m = -1\), we can use the point-slope form of the line's equation, which is:

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

Using the point \((-4, 8)\):

\[
y - 8 = -1(x + 4)
\]

Simplifying this gives:

\[
y - 8 = -x - 4
\]
\[
y = -x - 4 + 8
\]
\[
y = -x + 4
\]

Thus, the equation of the line that passes through the points \((-4, 8)\) and \((1, 3)\) is:

\[
y = -x + 4
\]

So, the correct answer is **y = -x + 4**.