By identifying the slope and y-intercept and using them to plot two key points, we were able to graph the line y = 7/5x. Remember, the slope tells you how steeply the line rises or falls, and the y-intercept tells you where the line crosses the y-axis.
Here's how to graph the line y = 7/5x using the slope and y-intercept:
1. Identify Slope and Intercept:
The equation is in slope-intercept form, y = mx + b, where:
m is the slope, which tells you how steeply the line rises or falls (positive for up, negative for down).
b is the y-intercept, which is the point where the line crosses the y-axis.
In this case, the slope (m) is 7/5, meaning the line rises 7 units for every 5 units it moves to the right. The y-intercept (b) is 0, indicating the line crosses the y-axis at (0, 0).
2. Plot the Y-Intercept:
Since the line passes through the point (0, 0), mark that point on the graph. This is your starting point.
3. Use the Slope to Plot Another Point:
Remember the slope tells you rise over run. Here, it's 7 up for every 5 to the right.
Rise: Move 7 units up from the y-intercept (0, 0).
Run: Move 5 units to the right from the y-intercept (0, 0).
This brings you to the point (5, 7). Mark this point on the graph.
4. Draw the Line:
Connect the y-intercept (0, 0) and the point you just plotted (5, 7) with a straight line. This is the graph of y = 7/5x!