From the image, we see a problem where you are asked to determine the equation of a line on a coordinate plane. The equation needs to be in the form $y = mx + b$, where:

• $m$ is the slope of the line, and
• $b$ is the y-intercept (where the line crosses the y-axis).

Step-by-step Solution:

1. Find the slope $m$: The slope of a line is calculated using the formula: $m = \frac{\text{rise}}{\text{run}}$ From the graph:

   • The line rises by $+2$ (vertical change) when moving to the right by $+1$ (horizontal change).
   • Therefore, the slope is: $m = \frac{2}{1} = 2$

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 $(0, -4)$. Hence, $b = -4$.

3. Write the equation of the line: Substituting $m = 2$ and $b = -4$ into the equation $y = mx + b$, we get: $y = 2x - 4$

Final Answer:

The equation of the line is: $y = 2x - 4$

Let me know if you want more clarification or have questions! Below are related questions and a tip for working with linear equations.

Related Questions:

1. How can you calculate the slope of a line using two points on the graph?
2. What is the significance of the y-intercept in real-world problems?
3. How do you find the equation of a line if given a point and a slope?
4. Can two different lines have the same slope? What does that mean graphically?
5. How do you graph a line using just the slope and y-intercept?

Tip:

When finding the slope, always pick two distinct points on the graph where the coordinates are easy to read. This reduces errors in calculation!