HomeGraphing Review Worksheet: Plotting, Slope, Intercepts, and Reading Lines Free original lessons
Graphing Review Worksheet: Plotting, Slope, Intercepts, and Reading Lines
A planned two-page review with 15 items covering plotting points, slope from a graph, intercepts, and reading a line graph, plus answer key with plotted lines and explanations.
Free lesson
Four exercises
Worked answers
Algebra and Function Practice
This review set spans four core graphing skills: plotting ordered pairs, finding slope from a graphed line, identifying x- and y-intercepts, and reading a line graph to answer a question. It excludes inequalities and nonlinear functions. All items use simple integer coordinates and consistent units so results are easy to check. The planned worksheet contains 15 items across four sections, with an answer key that includes plotted lines and brief explanations. Use the worked example and practice tasks below to prepare, then adapt the planned two-page review to your class.
Practice materials: Printable downloads are not available for this lesson yet. Use the instructions and four exercises below.
Plotting Points on the Coordinate Plane
An ordered pair (x, y) tells you how far to move horizontally from the origin and then how far to move vertically. Move right for positive x, left for negative x, up for positive y, and down for negative y. Plot the point where those two moves meet.
Always label each plotted point with its coordinates so a reader can verify your work. A common convention is to write the pair next to the dot, using a small arrow if space is tight. Because handwriting varies, accept any clear label that unambiguously matches the dot.
- Start at the origin (0, 0).
- Move along the x-axis by the first number: right if positive, left if negative.
- Move parallel to the y-axis by the second number: up if positive, down if negative.
- Mark the point and label it with its ordered pair.
Finding Slope from a Graph
Slope measures steepness and direction: rise over run, or change in y divided by change in x. Choose two points on the line whose coordinates are easy to read, such as where the line crosses grid intersections.
Count the vertical change (rise) and the horizontal change (run) from one point to the other. Keep the sign: rising left to right gives positive slope, falling gives negative slope. A horizontal line has slope 0; a vertical line has undefined slope.
- Pick two clear points on the line and record their coordinates.
- Subtract y-values to get the rise; subtract x-values in the same order to get the run.
- Divide rise by run and simplify the fraction.
- Check the sign against the visual direction of the line.
Identifying Intercepts
The y-intercept is where the line crosses the y-axis; its x-coordinate is 0. The x-intercept is where the line crosses the x-axis; its y-coordinate is 0. Read intercepts directly from the graph when the crossing is clear, or compute them from an equation by substituting 0 for the other variable.
State intercepts as ordered pairs, for example (0, 3) and (4, 0), so the location is unambiguous. If a line passes through the origin, both intercepts are (0, 0).
- To find the y-intercept, set x = 0 and solve, or look where the line meets the y-axis.
- To find the x-intercept, set y = 0 and solve, or look where the line meets the x-axis.
- Write each intercept as an ordered pair.
- Verify by checking that both points lie on the line.
Reading a Line Graph to Answer a Question
Reading a graph means connecting a value on one axis to the corresponding value on the other. Locate the given input on the horizontal axis, move vertically to the line, then move horizontally to the vertical axis to read the output.
Check the scale of each axis before reading. If each grid square represents 2 units, a point two squares up means 4 units, not 2. State units in your answer when the graph provides them.
- Identify what each axis represents and note the scale.
- Locate the given value on the correct axis.
- Move to the line, then to the other axis.
- Read the value using the scale and include units if given.
Worked example
A line passes through (1, 2) and (4, 8). Find its slope, y-intercept, and x-intercept, and state whether the line rises or falls from left to right.
Worked answer
Slope = (8 - 2) / (4 - 1) = 6 / 3 = 2. Using y = 2x + b with (1, 2): 2 = 2(1) + b, so b = 0. The y-intercept is (0, 0). Setting y = 0: 0 = 2x, so x = 0; the x-intercept is also (0, 0). The slope is positive, so the line rises from left to right.
Four practice exercises
Exercise 1
Plot the points A(2, 3), B(-1, 4), and C(0, -2) on a coordinate plane. Describe where each point lies relative to the axes.
Show answer and check
A is 2 right and 3 up from the origin, in the first quadrant. B is 1 left and 4 up, in the second quadrant. C is on the y-axis, 2 down from the origin.
Why: For each ordered pair, move along x first, then along y. A has both coordinates positive; B has negative x and positive y; C has x = 0, so it lies on the y-axis.
Check: Verify that A is right and up, B is left and up, and C has no horizontal movement. Confirm each label matches its dot.
Exercise 2
A line on a grid passes through (-2, 1) and (2, 5). Find the slope and state whether the line rises or falls from left to right.
Show answer and check
Slope = (5 - 1) / (2 - (-2)) = 4 / 4 = 1. The line rises from left to right.
Why: Subtract y-values in the same order as x-values: 5 - 1 = 4 and 2 - (-2) = 4. The quotient is 1. A positive slope means the line rises.
Check: From (-2, 1), move up 4 and right 4 to reach (2, 5). The rise and run match the computed slope.
Exercise 3
A line has equation y = -3x + 6. Find the x-intercept and y-intercept as ordered pairs.
Show answer and check
y-intercept: (0, 6). x-intercept: (2, 0).
Why: Set x = 0: y = -3(0) + 6 = 6, giving (0, 6). Set y = 0: 0 = -3x + 6, so 3x = 6 and x = 2, giving (2, 0).
Check: Substitute each pair into the equation: (0, 6) gives 6 = 6; (2, 0) gives 0 = -6 + 6. Both are true.
Exercise 4
A line graph shows distance in kilometers on the vertical axis and time in hours on the horizontal axis. Each grid square represents 1 hour horizontally and 5 kilometers vertically. The line passes through (0, 0) and (3, 15). What distance is shown at 4 hours, and what is the slope in kilometers per hour?
Show answer and check
At 4 hours the distance is 20 kilometers. The slope is 15 / 3 = 5 kilometers per hour.
Why: The line rises 15 kilometers over 3 hours, so the rate is 5 kilometers per hour. Extending the pattern, 4 hours corresponds to 4 × 5 = 20 kilometers. On the grid, 4 hours is 4 squares right and 20 kilometers is 4 squares up, so the point (4, 20) lies on the line.
Check: Confirm the scale: 4 squares up at 5 kilometers per square equals 20 kilometers. Check that 20 / 4 = 5, matching the slope.
Common mistakes
- Plotting (3, -2) by moving down 3 and right 2. Use the order (x, y): move 3 right, then 2 down. Label the point to confirm.
- Computing slope as run over rise. Slope is rise over run: change in y divided by change in x. Count vertical change first, then horizontal.
- Writing an intercept as a single number such as 4 instead of (4, 0). Intercepts are points; give both coordinates as an ordered pair.
- Ignoring the axis scale when reading a graph. Check how many units each grid square represents before reading the value.
Self-check rubric
- Plotting: each point is placed at the correct ordered pair and labeled clearly; accept any legible label that unambiguously matches the dot.
- Slope: rise and run are computed from two clear points with consistent subtraction order; fraction is simplified and sign matches the line's direction.
- Intercepts: both intercepts are given as ordered pairs and lie on the line.
- Graph reading: the correct axis and scale are used, and units are included when the graph provides them.
- Explanation: reasoning is shown in at least one sentence or a clear calculation for each item.
Questions and answers
How many items are planned for the review?
The planned two-page review contains 15 items across four sections: plotting points, finding slope from a graph, identifying intercepts, and reading a line graph.
Does the review include inequalities or nonlinear functions?
No. The boundary excludes inequalities and nonlinear functions; all lines are straight.
What does the answer key include?
The planned key includes plotted lines and brief explanations so students can check reasoning, not just final values.
How should intercepts be written?
As ordered pairs such as (0, 3) and (4, 0). A single number does not show which axis the intercept lies on.