Linear Function Word Problems

Linear function word problems describe a real situation that changes at a constant rate, then ask you to model it with a line and answer a question. The skill is translation: turn the words into an equation of the form y = mx + b, where m is the rate of change (slope) and b is the starting value (y-intercept). From there you can graph it or read off slope-intercept form.

Suppose a gym charges a $20 fee to join plus $5 for each visit. The total cost is C = 5x + 20, where x is the number of visits. The $20 fee is the y-intercept (the cost before any visits) and the $5 per visit is the slope (how fast the cost rises).

Once the line is drawn, the graph answers questions directly. To find the cost of 4 visits, go to x = 4 and read the height: C = 5(4) + 20 = $40. To find how many visits cost $45, set 45 = 5x + 20 and solve for x. Building the line from a table of points is covered in graphing linear functions using a table of values.

• Identify the constant rate — this is the slope, m.
• Identify the starting or fixed value — this is the y-intercept, b.
• Write the equation y = mx + b and graph or solve it.

The same approach handles distance, cost, and savings problems — see more in the application of linear relations.

Related lessons

• Algebra