To graph a line with a given slope and a specific point, you can follow a simple process. In this case, the slope (m) is 7, and the point through which the line passes is (2, 9).
Step 1: Understand the Slope
The slope of a line measures how steep the line is, calculated as the rise over the run. A slope of 7 means that for every 1 unit you move to the right (horizontal direction), the line rises 7 units (vertical direction).
Step 2: Plot the Point
Start by plotting the point (2, 9) on your graph. Go 2 units right along the x-axis and 9 units up along the y-axis. Make sure to mark this point clearly.
Step 3: Use the Slope to Find Another Point
From the point (2, 9), use the slope to find another point on the line. Since the slope is 7, you will move 1 unit to the right (to x = 3) and 7 units up from the point (2, 9). This will take you to the point (3, 16).
Step 4: Draw the Line
Once you have both points plotted, you can draw a straight line through them. Use a ruler to ensure the line is straight. Extend the line in both directions, adding arrows on each end to indicate that it continues infinitely.
Step 5: Label the Line
It can be helpful to label the line with its equation. Since you have the slope and a point, you can use the point-slope form of a line’s equation, which is y – y1 = m(x – x1). Plugging in the values yields:
y – 9 = 7(x – 2)
This can be rearranged into slope-intercept form (y = mx + b) if desired.
Conclusion
By following these steps, you can easily graph a line with a slope of 7 passing through the point (2, 9). Happy graphing!