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.