a straight line goes through (-9,15) and (3,11). Whats the line's equation?

To find the equation of the line passing through the points \((-9, 15)\) and \((3, 11)\), we need to use the **point-slope form** of a linear equation:

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

### Step 1: Find the slope (m)
The slope \(m\) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

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

Substitute the given points \((-9, 15)\) and \((3, 11)\) into the formula:

\[
m = \frac{11 - 15}{3 - (-9)} = \frac{-4}{3 + 9} = \frac{-4}{12} = -\frac{1}{3}
\]

### Step 2: Use point-slope form
Now that we have the slope \(m = -\frac{1}{3}\), we can use the point-slope form. Using one of the given points, say \((3, 11)\):

\[
y - 11 = -\frac{1}{3}(x - 3)
\]

### Step 3: Simplify to slope-intercept form
Now simplify the equation to get it into slope-intercept form \(y = mx + b\):

\[
y - 11 = -\frac{1}{3}(x - 3)
\]

Distribute the \(-\frac{1}{3}\):

\[
y - 11 = -\frac{1}{3}x + 1
\]

Add 11 to both sides to solve for \(y\):

\[
y = -\frac{1}{3}x + 1 + 11
\]

\[
y = -\frac{1}{3}x + 12
\]

### Final Answer:
The equation of the line is:

\[
y = -\frac{1}{3}x + 12
\]

Would you like more details on any part of the solution? 

Here are 5 related questions you might find useful:
1. How do you find the equation of a line given its slope and one point?
2. What is the slope of a vertical line?
3. How can you convert a line from slope-intercept to point-slope form?
4. How do you determine if two lines are parallel?
5. How do you find the y-intercept from an equation?

**Tip:** The slope of a line measures how steep the line is. A negative slope means the line goes downwards as you move to the right!

A straight line goes through (-9,15) and (3,11). What's the line's equation?

Discover how to find the equation of a line passing through the points (-9, 15) and (3, 11) using algebraic concepts like slope-intercept and point-slope form. This guide provides a step-by-step solution, suitable for Grades 8-10.

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