Grade 8 · Functions · MAT-08-FN-009
Write Linear Equations from Data and Graphs
Represent and solve write linear equations from data and graphs problems using precise mathematical notation, multiple representations, and justified reasoning.
Learning objectives
What you should be able to do
- Represent and solve write linear equations from data and graphs problems using precise mathematical notation, multiple representations, and justified reasoning.
- Interpret and verify write linear equations from data and graphs results in context, including units, constraints, and reasonableness.
Prerequisite check
Make sure the foundation is ready.
Grade 8 uses this prerequisite as active knowledge in a more formal representation.
Learn
Build the idea from meaning, not memorization.
Meaning and structure
Write Linear Equations from Data and Graphs belongs to functions. Identify the governing property or relationship before choosing a procedure.
Multiple representations
Represent write linear equations from data and graphs numerically and symbolically, then connect it to the Grade 8 Math Box. Tables, graphs, equations, coordinate models, diagrams, and verbal descriptions must agree.
Verification and interpretation
Check with substitution, an inverse operation, an equivalent representation, geometric invariants, estimation, or context. State whether the result is exact or approximate and preserve relevant units and constraints.
Math Box · Interactive lesson
Touch the math. Change it. See what stays true.
Use the interactive model before and after the worked examples. Change the inputs, make a prediction, then use the model to test whether your reasoning holds.
Linear Function Lab
- Model write linear equations from data and graphs in the Math Box.
- Change one input and predict which quantities or invariants should change.
- Explain what the visual, equation, and numerical result say about the same relationship.
Worked examples
Twenty different ways to see the concept work.
A line has slope 1 and y-intercept 3. Write its equation.
y = 1x + 3Slope-intercept form records rate and starting value.
A line has slope 2 and y-intercept 5. Write its equation.
y = 2x + 5Slope-intercept form records rate and starting value.
A line has slope 3 and y-intercept 7. Write its equation.
y = 3x + 7Slope-intercept form records rate and starting value.
A line has slope 4 and y-intercept 9. Write its equation.
y = 4x + 9Slope-intercept form records rate and starting value.
A line has slope 5 and y-intercept 11. Write its equation.
y = 5x + 11Slope-intercept form records rate and starting value.
A line has slope 6 and y-intercept 13. Write its equation.
y = 6x + 13Slope-intercept form records rate and starting value.
A line has slope 7 and y-intercept 15. Write its equation.
y = 7x + 15Slope-intercept form records rate and starting value.
A line has slope 8 and y-intercept 17. Write its equation.
y = 8x + 17Slope-intercept form records rate and starting value.
A line has slope 9 and y-intercept 19. Write its equation.
y = 9x + 19Slope-intercept form records rate and starting value.
A line has slope 10 and y-intercept 21. Write its equation.
y = 10x + 21Slope-intercept form records rate and starting value.
A line has slope 11 and y-intercept 23. Write its equation.
y = 11x + 23Slope-intercept form records rate and starting value.
A line has slope 12 and y-intercept 25. Write its equation.
y = 12x + 25Slope-intercept form records rate and starting value.
A line has slope 13 and y-intercept 27. Write its equation.
y = 13x + 27Slope-intercept form records rate and starting value.
A line has slope 14 and y-intercept 29. Write its equation.
y = 14x + 29Slope-intercept form records rate and starting value.
A line has slope 15 and y-intercept 31. Write its equation.
y = 15x + 31Slope-intercept form records rate and starting value.
A line has slope 16 and y-intercept 33. Write its equation.
y = 16x + 33Slope-intercept form records rate and starting value.
A line has slope 17 and y-intercept 35. Write its equation.
y = 17x + 35Slope-intercept form records rate and starting value.
A line has slope 18 and y-intercept 37. Write its equation.
y = 18x + 37Slope-intercept form records rate and starting value.
A line has slope 19 and y-intercept 39. Write its equation.
y = 19x + 39Slope-intercept form records rate and starting value.
A line has slope 20 and y-intercept 41. Write its equation.
y = 20x + 41Slope-intercept form records rate and starting value.
Practice
Guided practice with hints
01A line has slope 21 and y-intercept 43. Write its equation.
Hint: Represent the structure first, calculate carefully, then verify with a second representation or substitution.
Answer: y = 21x + 43
02A line has slope 22 and y-intercept 45. Write its equation.
Hint: Represent the structure first, calculate carefully, then verify with a second representation or substitution.
Answer: y = 22x + 45
03A line has slope 23 and y-intercept 47. Write its equation.
Hint: Represent the structure first, calculate carefully, then verify with a second representation or substitution.
Answer: y = 23x + 47
04A line has slope 24 and y-intercept 49. Write its equation.
Hint: Represent the structure first, calculate carefully, then verify with a second representation or substitution.
Answer: y = 24x + 49
05A line has slope 25 and y-intercept 51. Write its equation.
Hint: Represent the structure first, calculate carefully, then verify with a second representation or substitution.
Answer: y = 25x + 51
06A line has slope 26 and y-intercept 53. Write its equation.
Hint: Represent the structure first, calculate carefully, then verify with a second representation or substitution.
Answer: y = 26x + 53
Practice
Independent practice
01A line has slope 27 and y-intercept 55. Write its equation.
Answer: y = 27x + 55
02A line has slope 28 and y-intercept 57. Write its equation.
Answer: y = 28x + 57
03A line has slope 29 and y-intercept 59. Write its equation.
Answer: y = 29x + 59
04A line has slope 30 and y-intercept 61. Write its equation.
Answer: y = 30x + 61
05A line has slope 31 and y-intercept 63. Write its equation.
Answer: y = 31x + 63
06A line has slope 32 and y-intercept 65. Write its equation.
Answer: y = 32x + 65
07A line has slope 33 and y-intercept 67. Write its equation.
Answer: y = 33x + 67
08A line has slope 34 and y-intercept 69. Write its equation.
Answer: y = 34x + 69
Common mistakes
Learn to catch the error, not just the answer.
Outputs may repeat; one input cannot have two different outputs.
Slope is change per unit; intercept is output at x=0.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Model constant rates and starting values with tables, graphs, and equations.
- Compare functions by rate of change and initial value.
Challenge problems
A line has slope 35 and y-intercept 71. Write its equation.
y = 35x + 71
A line has slope 36 and y-intercept 73. Write its equation.
y = 36x + 73
A line has slope 37 and y-intercept 75. Write its equation.
y = 37x + 75
A line has slope 38 and y-intercept 77. Write its equation.
y = 38x + 77
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Grade 8 Algebra & Modeling Sprint
Solve write linear equations from data and graphs problems and justify each result with a valid verification method.
Practice
Mastery check
01A line has slope 39 and y-intercept 79. Write its equation.
Answer: y = 39x + 79
02A line has slope 40 and y-intercept 81. Write its equation.
Answer: y = 40x + 81
03A line has slope 41 and y-intercept 83. Write its equation.
Answer: y = 41x + 83
04A line has slope 42 and y-intercept 85. Write its equation.
Answer: y = 42x + 85
05A line has slope 43 and y-intercept 87. Write its equation.
Answer: y = 43x + 87
06A line has slope 44 and y-intercept 89. Write its equation.
Answer: y = 44x + 89
07A line has slope 45 and y-intercept 91. Write its equation.
Answer: y = 45x + 91
08A line has slope 46 and y-intercept 93. Write its equation.
Answer: y = 46x + 93
Terminology
Words to know
- function
- A relation assigning exactly one output to each input.
- slope
- Vertical change divided by horizontal change for a nonvertical line.
- y-intercept
- The output where a graph crosses the y-axis.
- rate of change
- Output change per unit input change.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
California Mathematics Framework (2023)
Grade 8 instructional guidance, mathematical practices, modeling, and progression toward high-school mathematics.Common Core State Standards for Mathematics — Grade 8
Grade-level expectations for real numbers, equations, functions, geometry, and statistics.Principles to Actions: Ensuring Mathematical Success for All
Research-informed emphasis on reasoning, representations, discourse, productive struggle, and conceptual understanding.