Formulas: Linear Relationships [TEKS Tools Grade 8]

This post specifically looks at how formulas can be used solve problems involving linear relationships, including the form y = mx + b. Read more about TEKS Tools and their rationale here.

Formulas

Formulas account for around 38% of each 8th grade STAAR test. These formulas are applied to solve problems related to volume, surface area, triangles, similar shapes, linear relationships, and finances.

The main function of a formula is to understand the relationship between quantities. In fourth grade, students were first introduced to the formulas for area and perimeter of squares and rectangles. In fifth grade, they were introduced to the formula for volume of a rectangular prism. In sixth grade, the formulas for area of a triangle, parallelogram, and trapezoid are explored. In 7th grade, students are introduced to surface area and to circle geometry, exploring π (pi), circumference, and area. Now in 8th grade, students stabilize their previous learning about linear relationships, surface area, volume (including composite shapes), and finances while beginning to explore geometric concepts such as the Pythagorean Theorem.

Slope and y-intercept

8.4C - use data from a table or graph to determine the rate of change or slope and y- intercept in mathematical and real-world problems

2023-24: a graph of a line was given, students had to identify the slope and y-intercept

2023-32: a table and verbal description was given, students had to identify the slope and y-intercept in context

2024-15: a table and verbal description was given, students had to identify the y-intercept in context

2024-29: a table was given, students had to identify the slope and y-intercept

2025-5: a graph of a line was given, students had to identify the slope and y-intercept

2025-30: a table and verbal description was given, students had to identify the slope and y-intercept in context

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8.5A - represent linear proportional situations with tables, graphs, and equations in the form of y = kx

2023-39: a proportional relationship was given, students had to represent it with an equation

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8.5H - identify examples of proportional and non-proportional functions that arise from mathematical and real-world problems

2025-12: two verbal descriptions and two tables were given, students had to identify the proportional relationship

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8.5I - write an equation in the form y = mx + b to model a linear relationship between two quantities using verbal, numerical, tabular, and graphical representations

2023-20: a linear function was graphed, students had to write the equation

2023-29: a linear function was graphed, students had to write the equation

2024-5: a linear relationship was displayed in a table, students had to write the equation

2025-16: two points in a linear relationship were given, students had to write the equation