Graphing Linear Equations

Use Finch to model linear equations using slope-intercept form.

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BEGINNER: Outputs Only

Required lessons: Moving & Turning

Students will graph linear equations by programming the Finch to start at the y-intercept and repeatedly move according to the slope (rise over run).


  1. Mark the origin and axes of your centimeter coordinate grid.
  2. Give students a linear equation and have them identify the slope and y-intercept.
  3. Put a marker in Finch’s marker hole and place the tip of the marker on the y-intercept. Make sure Finch’s beak is aligned with the y-axis in order to create an accurate graph.
  4. Program Finch to move forward “rise” and right “run” centimeters at 10% speed. Repeat 3 to 5 times. To increase accuracy, place wait/pause blocks after each move and turn.
    • Note: moving forward negative centimeters will make Finch move backward. Try this on your equations with negative slopes!
  5. Once Finch has drawn the steps, remove Finch from the graph and draw your line using a yardstick.

Tip: Reduce Finch’s speed to 10% or less to increase accuracy.

ADVANCED: Going Further

Required lessons: Variables

The same lesson above can be completed using variables! Create variables for rise and run to use in the loop and move forward blocks. 


  • Butcher paper or poster board
  • Ruler with cm OR use our new Finch Math Mat for your coordinate plane!


Understand the connections between proportional relationships, lines, and linear equations.
Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

Analyze and solve linear equations and pairs of simultaneous linear equations.
Solve linear equations in one variable.

Define, evaluate, and compare functions.
3. Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.

Use functions to model relationships between quantities.
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.