Graph the line with slope 12 passing through the point −3, 5.

To graph the line with slope 12 passing through the point −3, 5, we can follow these steps:

1. Plot the given point on the coordinate plane. The point −3, 5 represents the x-coordinate of -3 and the y-coordinate of 5. Mark this point on the graph.

2. Use the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept.

3. Since the slope is given as 12, we can substitute this value into the equation as y = 12x + b.

4. To find the value of b, we can use the given point −3, 5. Substitute the x-coordinate of -3 and the y-coordinate of 5 into the equation and solve for b.

   5 = 12(-3) + b 5 = -36 + b b = 41

5. Now that we have the equation y = 12x + 41, we can plot additional points on the graph using different x-values and then connect them to form the line.

6. Choose a few x-values, such as -4, 0, and 2, and substitute them into the equation to find the corresponding y-values.

   For x = -4: y = 12(-4) + 41 = -48 + 41 = -7 For x = 0: y = 12(0) + 41 = 0 + 41 = 41 For x = 2: y = 12(2) + 41 = 24 + 41 = 65

7. Plot these points (-4, -7), (0, 41), and (2, 65) on the graph.

8. Finally, connect the points with a straight line. This line represents the graph of the equation y = 12x + 41.

Note: The graph should show a line that passes through the point (-3, 5) and has a steep positive slope.