Linear functions
Finding slope from graphs worksheets
Read eight graphed lines and find each exact slope. Use the coordinate scale to compare rise and run, then check a separate answer key with worked calculations.
Preview and downloadOne relationship, several ways to see it
Linear functions worksheets
Find a slope, read an intercept, write an equation and draw its graph. Connect these skills with focused practice, then extend a line into the solution region of an inequality.
Choose a worksheetFrom points to an equation
- Two points on the line(0, 1) and (2, 2)
- Rise divided by runm = (2 − 1)/(2 − 0) = 1/2
- The y-axis crossing is 1y = (1/2)x + 1
Connect a value, an equation and a graph
Find and interpret slope
Read a line on a graph, calculate a rate of change from points, then identify the same property in an equation.
Linear functions
Finding slope from two points worksheets
Calculate exact slopes from ten pairs of integer-coordinate points. Practice signed differences and reduced fractions, with a separate key that explains the slope calculation.
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Linear functions
Slope and y-intercept from equations worksheets
Find slope and y-intercept in ten linear equations. Choose slope-intercept form, standard form or both, and practice slope alone or both properties with exact answers.
Preview and downloadConnect a value, an equation and a graph
Build a graph from given information
Use an equation, an intercept and point, or two points to draw the same kind of mathematical object: a complete straight line.
Linear functions
Graphing slope-intercept form worksheets
Graph eight lines in slope-intercept form. Choose graphing alone, graphing with slope and intercept questions, or writing an equation and graph from supplied properties.
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Linear functions
Graphing lines from an intercept and point worksheets
Construct eight lines from a supplied y-intercept and one ordered pair. Choose graphing alone or also find the slope and equation, with worked keys and completed graphs.
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Linear functions
Graphing lines from two points worksheets
Graph eight lines using two ordered pairs and a supplied y-intercept. Choose graphing alone or also calculate the slope and write an equation, with separate worked answers.
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Linear functions
Graphing standard-form equations worksheets
Graph eight equations in standard form Ax + By = C. Choose graphing alone or also find slope and label the y-intercept, using exact fractional slopes and worked keys.
Preview and downloadConnect a value, an equation and a graph
Connect graphs, properties and equations
Write equations from visible graphs or combine several representations in one mixed practice set.
Linear functions
Mixed linear equation skills worksheets
Connect graphs, equations and line properties in ten tasks: four graph-to-slope questions, four equation-to-slope questions and two write-and-graph problems.
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Linear functions
Writing linear equations from graphs worksheets
Write slope-intercept equations for eight graphed lines. Read the y-intercept, calculate an exact slope and check the equation against visible points with a separate worked key.
Preview and downloadConnect a value, an equation and a graph
Extend a line into a solution region
Use a boundary line and a shaded half-plane to describe the ordered pairs that satisfy a two-variable inequality.
Linear functions
Graphing two-variable inequalities worksheets
Graph eight linear inequalities on coordinate planes. Select any nonempty combination of <, ≤, > and ≥, then draw the boundaries and shade the solution regions with a separate graphical key.
Preview and downloadConnect a value, an equation and a graph
Connect equations and V-shaped graphs
Extend coordinate graphing to translations and reflections of absolute value functions. Read a vertex and opening direction, or construct the two branches from an equation.
Linear functions
Graphing absolute value functions worksheets
Graph eight absolute value functions or write equations from eight V-shaped graphs. Practice translations and reflections of y = |x| with integer vertices and a separate worked graphical key.
Preview and downloadChoose by readiness
Coordinate reading, signed subtraction and fraction fluency are separate prerequisites. Use a focused task to find which connection needs practice before choosing a mixed worksheet.
Read a rate of change from a graph
Begin after coordinate plotting and signed subtraction are secure. Compare vertical and horizontal changes between two points.
Open this starting point →Read the two properties before rearranging
Start with y already isolated so the learner can connect its coefficient and constant with a graph.
Open this starting point →Use a slope and an intercept
Write the equation and graph it from supplied properties, keeping each representation connected.
Open this starting point →Compare equation forms
Mix standard and slope-intercept forms after equivalent transformations and fractions are familiar.
Open this starting point →Keep slope and intercept distinct
The slope describes a change between points. The y-intercept is where the line meets the y-axis. In y = mx + b, m gives the slope and b gives the intercept value; (0, b) is the corresponding point.
For y = −2x + 3, the line crosses the y-axis at (0, 3). Moving one unit right lowers y by two. Both (1, 1) and (2, −1) lie on the same line. Check those coordinates before relying on how steep a picture looks.
These practice sets use finite, nonzero slopes. More generally, a horizontal line has slope zero, while a vertical line has undefined slope and cannot be written as y = mx + b.
Change the form, keep the line
2x + 3y = 6 and y = −(2/3)x + 2 describe the same ordered pairs. Rearranging changes how the equation is written; it does not move its graph. A line drawn from either form should pass through (0, 2) and (3, 0).
Have learners check one point in the original equation after they convert it. This catches sign and division mistakes more reliably than comparing two final formulas by appearance.
Connect the prerequisites
Apply a rule to inputs
Build a table of values before plotting the coordinate pairs and looking for a constant rate of change.
Function tables →Rearrange with equivalent operations
Practice inverse operations and signed fractions before isolating y in a standard-form equation.
Equation practice →Follow a learning sequence
Use expressions, equations and comparisons as a foundation for line relationships.
Pre-algebra sequence →