CCSS.Math.Content.8.F.B.4
The standard
Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
Common Core State Standards for Mathematics · Functions
What this standard means
Students need to build a linear function from a situation, table, graph, or two points. They should find the rate of change and starting value, then write an equation like y = mx + b. They also need to explain what the slope and y-intercept mean in the context, not just calculate them.
Mastery looks like moving smoothly among words, tables, graphs, points, and equations. Students often mix up x and y, subtract in the wrong order when finding slope, or name the y-intercept without explaining its real meaning. They may also think every table is linear without checking equal rates.
Ways to teach it
- Give pairs two coordinate points on cards and have them graph, find slope, find intercept, then write the matching equation.
- Ask students to explain: In y = 12x + 40 for a bike rental, what do 12 and 40 mean?
- Use a four-row table and ask students to find the rate, starting value, equation, and one sentence of context.
- Compare phone plans with a start-up fee and monthly cost, then write and graph equations for each plan.
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Related standards
- CCSS.Math.Content.HSF-BF.A
Build a function that models a relationship between two quantities
- CCSS.Math.Content.HSF-IF.B.4
For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs show...
- CCSS.Math.Content.8.F.B.5
Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or ...
- CCSS.Math.Content.HSF-LE.A.2
Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pa...