8.5.I
The Standard
write an equation in the form y = mx + b to model a linear relationship between two quantities using verbal, numerical, tabular, and graphical representations
Texas Essential Knowledge and Skills for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students translate a linear relationship from words, values, a table, or a graph into y = mx + b. They identify the rate of change m and starting value b from each representation.
What Mastery Looks Like
- Students correctly find m from two points, a table, a graph, or a stated rate. They find b, write the equation, and check that given values satisfy it.
Common Misconceptions
- Students may switch the slope and y-intercept, use total change instead of rate of change, or miss a negative slope. They may also use the first table value as b even when x is not zero.
How to Assess It
- Give students the points (2, 7) and (5, 16). Ask them to write y = mx + b and label what m and b mean.
Lesson moves
Ways to Teach It
Give pairs a graph, two colored rulers, and sticky notes to mark rise, run, and the y-intercept before writing the equation.
Ask students to explain why a table beginning at x = 3 does not necessarily show the y-intercept.
Play Equation Match with cards showing verbal situations, tables, graphs, and equations that students sort into matching sets.
Use a taxi fare with a starting fee and cost per mile, then have students write and interpret its equation.
Keep exploring
Related Standards
- 7.7
The student applies mathematical process standards to represent linear relationships using multiple representations. The student is expected to represent linear...
- 6.6.C
represent a given situation using verbal descriptions, tables, graphs, and equations in the form y = kx or y = x + b
- 8.5.B
represent linear non-proportional situations with tables, graphs, and equations in the form of y = mx + b, where b ≠ 0
- 8.5.A
represent linear proportional situations with tables, graphs, and equations in the form of y = kx
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