To graph a line with a given slope and a point, we can use the slope-intercept form of the equation of a line, which is given by:
y = mx + b
In this case, the slope (m) is 7 and the line passes through the point (2, 9). We will first determine the y-intercept (b) by substituting the point into the equation.
Substituting (x, y) = (2, 9) into the equation:
9 = 7(2) + b
9 = 14 + b
Now, solve for b:
b = 9 – 14
b = -5
Now that we have both the slope and the y-intercept, the equation of our line is:
y = 7x – 5
Next, we can graph the line. Start by plotting the point (2, 9) on the coordinate plane. Then, using the slope, which is 7 (or 7/1), we can find another point on the line. From (2, 9), move 7 units up (the rise) and 1 unit to the right (the run) to reach the point (3, 16).
Now you can draw a straight line through the points (2, 9) and (3, 16). Extend the line in both directions, and you’ve successfully graphed the line with slope 7 passing through the point (2, 9).