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Identify the slope and the y-intercept of the line graphed below. Then, write the equation of the line in slope-intercept form.


Let's analyze the graph to determine the slope, y-intercept, and equation of the line.

### Step 1: Identifying the Slope
From the graph, the line passes through two clear points. Let's use the points:
- Point 1: \( (0, -1) \)
- Point 2: \( (2, 1) \)

The slope formula is:
\[
\text{slope (m)} = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substitute the points \( (0, -1) \) and \( (2, 1) \):
\[
m = \frac{1 - (-1)}{2 - 0} = \frac{1 + 1}{2} = \frac{2}{2} = 1
\]
So, the slope \( m = 1 \).

### Step 2: Identifying the Y-Intercept
The y-intercept is where the line crosses the y-axis. From the graph, it is clear that the line crosses the y-axis at \( y = -1 \). So, the y-intercept \( b = -1 \).

### Step 3: Writing the Equation in Slope-Intercept Form
The slope-intercept form of a line is:
\[
y = mx + b
\]
Substituting \( m = 1 \) and \( b = -1 \):
\[
y = 1x - 1 \quad \text{or simply} \quad y = x - 1
\]

### Final Answer:
- **Slope**: \( m = 1 \)
- **Y-Intercept**: \( b = -1 \)
- **Equation of the Line**: \( y = x - 1 \)

Would you like further explanation or have any questions?

Here are 5 related questions to explore:
1. What is the slope of a line parallel to this one?
2. How do you find the equation of a line given two points?
3. How do you determine the slope if the line is vertical?
4. What does the slope of a line tell you about its steepness?
5. How do you graph a line using its slope and y-intercept?

**Tip**: In slope-intercept form, the slope \( m \) determines how steep the line is, and the y-intercept \( b \) tells where the line crosses the y-axis.

Identify the slope and the y-intercept of the line graphed below. Then, write the equation of the line in slope-intercept form.

Learn how to find the slope and y-intercept of a line by analyzing a graph. This problem covers key algebraic concepts, including slope-intercept form and slope calculation. Suitable for students in Grades 7-9.

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