Writing an equation and graphing a line given its slope and y-intercept Write an equation in slope-intercept form for the line with slope 7 and \( y \)-intercept -6. Then graph the line. Fauation.

Step 1. Write the Equation • In slope-intercept form, a line is written as y = mx + b, where m is the slope and b is the y-intercept. • Given m = 7 and b = -6, the equation is:   y = 7x – 6 Step 2. Graphing the Line 1. Start with the y-intercept:   Plot the point (0, -6) on the graph. 2. Use the slope to find another point:   Since the slope is 7, which means “rise over run” = 7/1, move up 7 units and 1 unit to the right.   From (0, -6), moving right 1 gives x = 1, and moving up 7 gives y = 1.   Plot the point (1, 1). 3. Draw the Line:   Use a ruler to draw a straight line through the points (0, -6) and (1, 1). Extend the line in both directions. Optional: Additional point check • If you plug x = -1 into the equation:   y = 7(-1) – 6 = -7 – 6 = -13.   So, the point (-1, -13) is also on the line. Below is a simple representation of the graph (not to scale): | 10 | | 8 | * (2,8) | 6 | | 4 | | 2 | * (1,1) | y-axis 0 |--------------------------- | -2 | | -4 | | -6 | * (0,-6) | -8 | | -10 | | -12 | | -14 | * (-1,-13) |__________________________ -2 -1 0 1 2 3 x-axis This graph shows the y-intercept at (0, -6) and another point at (1, 1). Connecting these points gives you the line described by y = 7x – 6. That’s it!