https://file.aiquickdraw.com/mathbot/file/1730039103814g8xyec5b.jpg

To find the equation of the red line shown on the graph, we can use the slope-intercept form of a line equation, which is:

\[
y = mx + b
\]

where \( m \) represents the slope, and \( b \) is the y-intercept.

### Step 1: Identify Two Points on the Line
From the graph, we can see that the line passes through:
- Point \( (2, 5) \)
- Point \( (5, 8) \)

### Step 2: Calculate the Slope (\( m \))
The formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

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

Plugging in the points \( (2, 5) \) and \( (5, 8) \):

\[
m = \frac{8 - 5}{5 - 2} = \frac{3}{3} = 1
\]

So, the slope \( m = 1 \).

### Step 3: Determine the Y-Intercept (\( b \))
To find \( b \), substitute one of the points (for example, \( (2, 5) \)) into the equation \( y = mx + b \) and solve for \( b \):

\[
5 = 1 \cdot 2 + b
\]
\[
5 = 2 + b
\]
\[
b = 3
\]

### Final Equation of the Line
With \( m = 1 \) and \( b = 3 \), the equation of the line is:

\[
y = x + 3
\]

Would you like further details or have any questions?

### Related Questions:
1. How do you determine the equation of a line given two points?
2. What is the slope-intercept form of a line?
3. How can you identify the slope of a line from a graph?
4. What does the y-intercept represent in a line equation?
5. How can you check if a point lies on a given line?

### Tip:
When working with linear equations, always verify the slope and intercept using multiple points if possible for accuracy.

Find the equation of the line shown on the graph.

Learn how to determine the equation of a line from a graph using the slope-intercept form. This example shows a line passing through points (2, 5) and (5, 8), allowing us to calculate the slope and y-intercept for the equation y = x + 3. Perfect for students in Grades 7-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation