Writing an Equation from a Graph
To write an equation from a graph in 6th grade, identify at least two exact grid intersection points that the line passes through, then determine the mathematical rule connecting the x and y values. If a line passes through (2, 8) and (3, 12), the output is always 4 times the input, giving y = 4x. If points are (0, 0), (5, 1), (10, 2), the output is x divided by 5, giving y = x/5. This reverse-engineering skill from Reveal Math, Course 1, Module 7 builds algebraic reasoning by moving from a visual graph back to its equation.
Key Concepts
Property To write the rule of a function from its graph, find the coordinates of points on the line and identify the mathematical operation that turns the input (x) into the output (y).
Examples A line passes through (2, 8) and (3, 12). The output y is 4 times the input x, so the rule is y = 4x. A graph contains the points (0, 0), (5, 1), and (10, 2). The output y is the input x divided by 5, so y = x / 5. If a line goes through (4, 3) and (8, 7), the output y is one less than the input x, so the equation is y = x 1.
Explanation Become a graph investigator! Scan the graphed line for exact points where it crosses the grid intersections perfectly.
Common Questions
How do I write an equation from a graph?
Identify at least two exact grid points that the line passes through. Compare the x and y values to find the pattern: is y always a multiple of x, or does a constant get added? Write the rule as an equation.
A graph passes through (0, 0) and (3, 9). What is the equation?
y = 3x, since 9 = 3 times 3. Check with another point: (1, 3) gives 3 = 3 times 1. Confirmed.
A graph passes through (4, 3) and (8, 7). What is the equation?
Going from x=4 to x=8, y goes from 3 to 7. The y is always 1 less than x: y = x - 1. Check: (4, 3) gives 4 - 1 = 3. Confirmed.
What if the line does not pass through the origin?
Look for a constant being added or subtracted. If y is always x + 5, the equation is y = x + 5, with an initial value of 5 (the y-value when x = 0).
How many points do I need to identify an equation from a graph?
Two points are enough to determine a linear equation, but checking a third point confirms your equation is correct.
When do 6th graders learn to write equations from graphs?
Module 7 of Reveal Math, Course 1 covers this in the Relationships Between Two Variables unit.