Find an equation in​ point-slope y minus y 1 equals m left parenthesis x minus x 1 right parenthesis for the line through the given points.
​(negative 4​,negative 11​) and ​(1​,4​)
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Part 1
What is the equation of the line in​ point-slope form?  
  
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​(Use integers or simplified fractions for any numbers in the​ equation.)

To find the equation of a line in **point-slope form**, we need the formula:

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

where \((x_1, y_1)\) is a point on the line and \(m\) is the slope of the line.

### Step 1: Find the slope \(m\)

The slope formula is:

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

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

\[
m = \frac{4 - (-11)}{1 - (-4)} = \frac{4 + 11}{1 + 4} = \frac{15}{5} = 3
\]

So, the slope \(m = 3\).

### Step 2: Use the point-slope formula

Now, we use one of the given points, say \((-4, -11)\), and the slope \(m = 3\) in the point-slope form equation:

\[
y - (-11) = 3(x - (-4))
\]

Simplify the equation:

\[
y + 11 = 3(x + 4)
\]

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

\[
y + 11 = 3(x + 4)
\]

This is the required equation in point-slope form.

Would you like further details, or do you have any questions?

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Here are five related questions you might consider:
1. How would you convert the point-slope form to slope-intercept form?
2. What happens if we use the other point \((1, 4)\) in the point-slope formula?
3. How do you interpret the slope in the context of these points?
4. What is the distance between the two given points?
5. How do you find the midpoint of the line segment between the two points?

**Tip:** The point-slope form is especially useful when you know a point on the line and the slope, as it gives you a direct equation without needing to rearrange it to other forms immediately.

Find an equation in point-slope y minus y1 equals m left parenthesis x minus x1 right parenthesis for the line through the given points (negative 4, negative 11) and (1, 4). What is the equation of the line in point-slope form? (Use integers or simplified fractions for any numbers in the equation.)

Learn how to find the equation of a line in point-slope form using the points (-4, -11) and (1, 4). This guide covers key algebraic concepts, including how to calculate the slope and use the point-slope formula. Suitable for students in Grades 8-10.

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