Let's find the equation of the line in the form $y = mx + b$, where:

• $m$ is the slope of the line
• $b$ is the y-intercept

Step 1: Determine the slope ($m$)

The slope formula is: $m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}$ From the graph, we can pick two points on the line. Let's use the points $(0, -3)$ and $(3, 3)$.

• The rise between these points is $3 - (-3) = 6$.
• The run is $3 - 0 = 3$.

Thus, the slope is: $m = \frac{6}{3} = 2$

Step 2: Determine the y-intercept ($b$)

The y-intercept is where the line crosses the y-axis. From the graph, we see that the line crosses the y-axis at $(0, -3)$. Therefore, $b = -3$.

Final Equation

The equation of the line is: $y = 2x - 3$

Would you like further clarification or additional details on this?

Here are 5 related questions for practice:

1. What is the slope of a line passing through points $(2, 3)$ and $(5, 7)$?
2. How do you find the x-intercept of a line given its equation?
3. How do you calculate the slope if you're given a horizontal line?
4. What is the equation of a line parallel to $y = 2x - 3$ but passing through $(1, 4)$?
5. How does the graph of $y = mx + b$ change when you modify $m$ or $b$?

Tip: When choosing points on a graph to calculate the slope, use points that lie exactly at grid intersections for greater accuracy.