What is an equation of the line that passes through the points left parenthesis, minus, 4, comma, 2, right parenthesis(−4,2) and left parenthesis, minus, 8, comma, minus, 2, right parenthesis(−8,−2)?

To find the equation of the line that passes through the points \((-4, 2)\) and \((-8, -2)\), we can use the point-slope form of the equation of a line:

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

First, we need to calculate the slope \(m\) using the formula:

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

Substituting the coordinates \((-4, 2)\) as \((x_1, y_1)\) and \((-8, -2)\) as \((x_2, y_2)\):

\[
m = \frac{-2 - 2}{-8 - (-4)} = \frac{-4}{-4} = 1
\]

Now that we have the slope \(m = 1\), we can use the point-slope form. Let's use the point \((-4, 2)\) for \((x_1, y_1)\):

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

Simplifying:

\[
y - 2 = x + 4
\]

Adding 2 to both sides to get the equation in slope-intercept form \(y = mx + b\):

\[
y = x + 6
\]

So, the equation of the line that passes through the points \((-4, 2)\) and \((-8, -2)\) is:

\[
y = x + 6
\]

Would you like more details on any step? Here are some related questions:

1. How do you find the slope if you have different coordinates?
2. What is the point-slope form of a line equation?
3. How can you convert between different forms of linear equations?
4. What is the importance of the slope in a linear equation?
5. How can you check if a point lies on a given line?

**Tip:** To verify your result, you can substitute the coordinates of both points into the final equation to ensure they satisfy it.

What is an equation of the line that passes through the points (-4, 2) and (-8, -2)?

Discover how to find the equation of a line that passes through the points (-4, 2) and (-8, -2) using key algebraic concepts such as the slope formula and point-slope form. This guide is perfect for students in Grades 8-10, offering a clear, step-by-step solution.

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