From the graph provided, we need to determine the equation of the line in slope-intercept form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Step 1: Identify two points on the line

Two visible points on the line are:

• Point 1: $(-4, -5)$
• Point 2: $(4, 3)$

Step 2: Calculate the slope $m$

The formula for the slope is: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substitute the points: $m = \frac{3 - (-5)}{4 - (-4)} = \frac{3 + 5}{4 + 4} = \frac{8}{8} = 1$

So, the slope $m = 1$.

Step 3: Find the y-intercept $b$

The y-intercept is the value of $y$ when $x = 0$. Looking at the graph, the line crosses the y-axis at $y = -1$. Hence, $b = -1$.

Final Equation

Substitute $m = 1$ and $b = -1$ into the slope-intercept form: $y = x - 1$

Answer:

The equation of the line is: $y = x - 1$

Would you like a further breakdown or explanation of this process?

Here are 5 related questions to deepen your understanding:

1. How do you determine the slope if the line is horizontal or vertical?
2. What does the slope of $1$ mean in terms of the angle of the line?
3. Can you derive the equation of a line in point-slope form and then convert it to slope-intercept form?
4. How would the equation change if the line were parallel to the one in the graph but passed through a different point?
5. How do you determine the equation of a line given only its graph and no labeled points?

Tip: When finding the slope, remember the order of subtraction (i.e., $y_2 - y_1$ and $x_2 - x_1$) is essential to avoid sign errors.