Example 1 : Elizabeth’s cell phone plan lets her choose how many minutes are included each month. The table shows the plan’s monthly cost y for a given number of included minutes x. Write an equation in slope-intercept form to represent the situation.
Step 1 : Notice that the change in cost is the same for each increase of 100 minutes. So, the relationship is linear.
Step 2 : Choose any two points in the form (x, y), from the table to find the slope :
For example, let us choose (100, 14) and (200, 20).
Use the slope formula.
m = (y2 - y1) / (x2 - x1)
Substitute (100, 14) for (x1, y1) and (200, 20) for (x2, y2).
m = (20 - 14) / (200 - 100)
m = 6 / 100
m = 0.06
Step 3 :
Find the y-intercept using the slope and any point from the table.
Slope-intercept form equation of a line :
y = mx + b
Plug m = 0.06, and (x, y) = (100, 14)
14 = 0.06(100) + b
14 = 6 + b
8 = b
Step 4 :
Now, plug m = 0.06 and b = 8 in slope-intercept form equation of a line.
y = mx + b
y = 0.06x + 8
