https://file.aiquickdraw.com/mathbot/file/1728238700304aqad0fuv.jpg

The equation of a straight line is typically written as:

\[
y = mx + b
\]

Where:
- \(m\) is the slope of the line.
- \(b\) is the y-intercept, the value where the line crosses the y-axis.

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

The slope \(m\) is calculated as:

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

From the graph, two clear points on the line are:
- Point 1: \((-6, -8)\)
- Point 2: \((0, -2)\)

Now calculate the slope:

\[
m = \frac{{-2 - (-8)}}{{0 - (-6)}} = \frac{{-2 + 8}}{{6}} = \frac{6}{6} = 1
\]

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

### Step 2: Find the y-intercept (\(b\))

The y-intercept is the point where the line crosses the y-axis. From the graph, the line crosses the y-axis at the point \((0, -2)\).

Thus, \(b = -2\).

### Conclusion:
\[
m = 1 \quad \text{and} \quad b = -2
\]

Would you like a more detailed explanation or have any other questions?

Here are five related questions:
1. How can the slope be negative, and what would it mean for the graph?
2. What would change if the y-intercept was positive?
3. How does changing the slope affect the steepness of the line?
4. What is the general formula for finding the slope between two points?
5. Can a line have a slope of zero, and how would that look on a graph?

**Tip:** To quickly find the slope of a line, remember that slope represents the "rise over run," or how much the line goes up or down compared to how much it moves horizontally!

Find the values of m and b from the graph of a straight line.

Learn how to determine the slope (m) and y-intercept (b) from the graph of a straight line. This step-by-step solution covers key linear algebra concepts and formulas, suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation