Question

Which of the following is the graph of this equation? y= 3 over 4 x + 2

Answer 1

To identify the graph of the equation \( y = \frac{3}{4}x + 2 \), let's break it down:

1. **Slope**: The slope (m) is \(\frac{3}{4}\), which means for every 4 units you move to the right (positive x-direction), you move up 3 units (positive y-direction).

2. **Y-intercept**: The y-intercept (b) is 2. This means the graph crosses the y-axis at the point (0, 2).

### Graphing Steps:
- Plot the y-intercept at the point (0, 2).
- From the y-intercept, use the slope to find another point.
- From (0, 2), move right 4 units to (4, 2) and then move up 3 units, reaching (4, 5).
- Draw a straight line through the points (0, 2) and (4, 5).

### Characteristics:
- The line will be ascending because the slope is positive.
- The line should continue infinitely in both directions.

### Conclusion:
To determine which graph corresponds to this line, look for a straight line that passes through (0, 2) and (4, 5) while ascending upwards to the right. If you are shown several graph options, locate the one that matches this description.