Write the equation of the line that passes through the points (−3,−7) and(9,1). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.

To find the equation of the line passing through the points \((-3, -7)\) and \((9, 1)\), we first need to calculate the slope of the line using the slope formula:

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

Substitute the given points \((-3, -7)\) and \((9, 1)\) into the formula:

\[
m = \frac{1 - (-7)}{9 - (-3)} = \frac{1 + 7}{9 + 3} = \frac{8}{12} = \frac{2}{3}
\]

Now that we have the slope \(m = \frac{2}{3}\), we use the point-slope form of the equation of a line:

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

We can use either point. Let's use \((-3, -7)\):

\[
y - (-7) = \frac{2}{3}(x - (-3))
\]

Simplifying:

\[
y + 7 = \frac{2}{3}(x + 3)
\]

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

\[
y + 7 = \frac{2}{3}(x + 3)
\]

Let me know if you'd like further details or explanations!

Here are 5 related questions to explore:
1. How can you convert this equation to slope-intercept form?
2. What is the equation if we use the point \((9, 1)\) instead?
3. How do we find the x-intercept of this line?
4. Can this equation be expressed in standard form?
5. What happens if the slope between two points is zero?

**Tip**: The point-slope form is very useful when you know one point and the slope of a line—it allows you to write the equation quickly without needing the y-intercept!

Write the equation of the line that passes through the points (−3,−7) and (9,1). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.

Learn how to find the equation of a line passing through the points (-3,-7) and (9,1) using the point-slope form. This problem covers key algebraic concepts like the slope formula and is suitable for students in Grades 8-10.

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