What is an equation of the line that passes through the points left parenthesis, minus, 1, comma, minus, 1, right parenthesis(−1,−1) and left parenthesis, 3, comma, 7, right parenthesis(3,7)?

To find the equation of the line passing through the points \((-1, -1)\) and \((3, 7)\), we can use the point-slope form of a line equation, which is:

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

Where:
- \(m\) is the slope of the line
- \((x_1, y_1)\) is a point on the line

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

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

Substituting the coordinates of the points \((-1, -1)\) and \((3, 7)\):

\[
m = \frac{7 - (-1)}{3 - (-1)} = \frac{7 + 1}{3 + 1} = \frac{8}{4} = 2
\]

### Step 2: Use the point-slope form
Now that we have the slope \(m = 2\), we can use either point \((-1, -1)\) or \((3, 7)\) in the point-slope form. Let's use the point \((-1, -1)\):

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

Simplifying:

\[
y + 1 = 2(x + 1)
\]

### Step 3: Simplify to slope-intercept form
Now, distribute the \(2\) on the right-hand side:

\[
y + 1 = 2x + 2
\]

Subtract 1 from both sides to get the equation in slope-intercept form (\(y = mx + b\)):

\[
y = 2x + 1
\]

### Final Answer:
The equation of the line passing through the points \((-1, -1)\) and \((3, 7)\) is:

\[
y = 2x + 1
\]

Would you like more details or have any questions?

Here are 5 related questions to explore further:
1. How do you find the equation of a line in point-slope form?
2. What is the meaning of the slope \(m\) in a line equation?
3. How do you convert a line equation from point-slope form to slope-intercept form?
4. What is the process for finding the equation of a line if given a slope and a point?
5. Can you derive the equation of a line if given its slope and the y-intercept?

**Tip:** Remember that the slope of a line describes how steep the line is, and it's calculated as the change in \(y\) over the change in \(x\).

What is an equation of the line that passes through the points (-1, -1) and (3, 7)?

Learn how to find the equation of the line passing through the points (-1, -1) and (3, 7). This solution explains how to use the slope formula, point-slope form, and slope-intercept form to arrive at the final answer, suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation