Linear Equation Word Problems – Notes + Homework

Students will define variables and identify the slope and y-intercept of a linear scenario from a graph.

Students will interpret the real-world meaning of a slope and a y-intercept in context, such as an hourly rate or a one-time fee.

Students will write a linear equation in slope-intercept form (y = mx + b) to model a word-problem scenario.

Students will use a linear equation to solve for an unknown cost, time, or starting value, including from two given data points instead of a graph.

Guided Notes Part 1 pairs each scenario with a printed graph, while several homework problems (the Twitter-followers and van-rental items) give only two data points and require students to derive the equation without a graph — sequence accordingly.

The bouncy-house, car-lease, and hat-collection problems on Homework Part 1 page 2 share the same fee-plus-rate structure, making them useful for quick repeated practice once the first is modeled together.

Have students check an algebraic solution against the printed graph in Guided Notes Part 1, since the notes explicitly ask whether the answer agrees with the graph.

Use the two-page Guided Notes sets for direct instruction first, then assign the matching homework set once students can identify slope and y-intercept independently.

Slope and y-intercept identification — students extract m and b from a graph or from two data points, as in the kayak-rental and Twitter-follower scenarios.

Contextual interpretation — students explain what a slope and y-intercept represent in a real situation, such as an hourly rate or a starting fee.

Equation writing in y = mx + b form — students build a linear equation from a described scenario before solving it.

Multi-step problem solving — students substitute values into their equation to find a cost, elapsed time, or starting amount, as in the candy, savings-account, and kickboxing-lesson problems.