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Part 1
Find an equation in​ point-slope y minus y 1 equals m left parenthesis x minus x 1 right parenthesisy−y1=mx−x1 for the line through the given points.
​(negative 4−4​,99​) and ​(11​,negative 1−1​)
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Part 1
What is the equation of the line in​ point-slope form?
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To find the equation of a line in **point-slope form** \( y - y_1 = m(x - x_1) \), we need two key components:  
1. A point on the line \((x_1, y_1)\)  
2. The slope of the line, \(m\), calculated using the two given points.

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### **Step 1: Find the Slope \(m\)**  
Using the formula for slope between two points \((x_1, y_1)\) and \((x_2, y_2)\):

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

Given points:  
\((-4, 9)\) and \((11, -1)\)

\[
m = \frac{-1 - 9}{11 - (-4)} = \frac{-10}{11 + 4} = \frac{-10}{15} = -\frac{2}{3}
\]

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### **Step 2: Use the Point-Slope Formula**  
The general point-slope form is:

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

We can use either of the given points. Let's use \((-4, 9)\). So, \(x_1 = -4\) and \(y_1 = 9\).

\[
y - 9 = -\frac{2}{3}(x - (-4))
\]

Simplify:

\[
y - 9 = -\frac{2}{3}(x + 4)
\]

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### **Final Answer: Equation in Point-Slope Form**

\[
y - 9 = -\frac{2}{3}(x + 4)
\]

You could also use the other point \((11, -1)\) and the equation would look slightly different, but both are equivalent.

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Would you like to see how to convert this into slope-intercept form?  

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Here are five related questions you might find interesting:  
1. How do you convert point-slope form to slope-intercept form?  
2. What is the equation of the line passing through the points \((2, 5)\) and \((6, 3)\)?  
3. How do you find the slope when given only the equation of a line?  
4. How does the slope of a vertical line differ from a horizontal line?  
5. What is the significance of the slope value being positive or negative?  

**Tip:** When working with point-slope form, always simplify carefully to avoid sign mistakes!

Find an equation in point-slope form for the line through the given points (-4, 9) and (11, -1).

Learn to find the point-slope form equation of a line through two points, (-4, 9) and (11, -1). This solution demonstrates calculating the slope and applying it to the point-slope form, covering essential algebra concepts for Grades 9-10.

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