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.