The equation of the line shown in the graph appears to have a positive slope, crossing the y-axis above the origin.

Looking at the options:

• F) $y = -1.5x + 3$ - This equation has a negative slope, so it does not match.
• G) $y = 2x - 1.5$ - This equation has a positive slope, but it appears to cross the y-axis at $-1.5$, which does not match the graph.
• H) $y = 3x + 2$ - This equation has a steep positive slope, but the y-intercept is 2.
• I) $y = 2x + 3$ - This equation has a positive slope of 2 and crosses the y-axis at 3, which matches the graph.

The correct answer is I) $y = 2x + 3$.

Would you like more details on why this is the case?

Here are five questions for further exploration:

1. What is the significance of the slope in a linear equation?
2. How does changing the y-intercept affect the graph of a line?
3. How do you determine the slope of a line from a graph?
4. What other forms can linear equations be written in besides slope-intercept form?
5. How can you tell if two lines are parallel by looking at their equations?

Tip: The slope of a line represents its steepness, and it can be found by dividing the change in y by the change in x (rise over run).