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Learn to plot linear graphs three ways: from tables, from x/y intercepts, and from slope plus a point. Includes worked example, practice tasks, and rubric.
Plotting linear graphs is a core algebra skill. This lesson teaches three reliable methods: building a table of values, using x- and y-intercepts, and starting from slope and a point. Each method produces the same straight line if done correctly. You will see a worked example, common mistakes, and four practice tasks with reasoning and checks. A planned worksheet with nine tasks and blank grids is described at the end.
Practice materials: Printable downloads are not available for this lesson yet. Use the instructions and four exercises below.
A table of values lists chosen x-values and the corresponding y-values from the equation. Plot each ordered pair (x, y) and connect the points with a straight line. Choose at least three x-values, including negative, zero, and positive, to confirm the pattern is linear.
For y = 2x + 1, a table with x = -1, 0, 1, 2 gives y = -1, 1, 3, 5. Plot (-1, -1), (0, 1), (1, 3), (2, 5). The points lie on a straight line with slope 2 and y-intercept 1.
The x-intercept is where the line crosses the x-axis (y = 0). The y-intercept is where it crosses the y-axis (x = 0). For 3x + 2y = 6, set y = 0 to get x = 2, and set x = 0 to get y = 3. Plot (2, 0) and (0, 3), then draw the line.
This method is fast when the equation is in standard form. If an intercept is fractional, plot it carefully or choose a third point to verify.
Slope m = rise/run describes vertical change per horizontal change. From a known point, move according to the slope to find another point. For y - 1 = 3(x - 2), the point is (2, 1) and slope is 3, so from (2, 1) move up 3 and right 1 to (3, 4). Plot both and draw the line.
Negative slopes move down as you go right. A slope of -1/2 means down 1, right 2. Always move consistently from the given point.
Plot the line y = -2x + 4 using a table of values with x = -1, 0, 1, 2.
Table: x=-1 gives y=6; x=0 gives y=4; x=1 gives y=2; x=2 gives y=0. Plot (-1,6), (0,4), (1,2), (2,0) and draw a straight line through them. The line has slope -2 and y-intercept 4.
Plot y = 3x - 2 using a table with x = -1, 0, 1, 2.
Points: (-1, -5), (0, -2), (1, 1), (2, 4). Draw a straight line through them.
Why: Substitute each x: 3(-1)-2=-5; 3(0)-2=-2; 3(1)-2=1; 3(2)-2=4. The constant slope 3 confirms a line.
Check: Plot a third point such as x=3 giving y=7; it should lie on the same line.
Plot 2x + 5y = 10 using x- and y-intercepts.
x-intercept: set y=0, 2x=10, x=5, point (5,0). y-intercept: set x=0, 5y=10, y=2, point (0,2). Draw the line through (5,0) and (0,2).
Why: Intercepts give two points quickly. Slope is -2/5, consistent with moving down 2 for every 5 right.
Check: Substitute a third point, e.g. x=2.5 gives y=1; check it lies on the drawn line.
Plot the line with slope 1/2 passing through (4, 1).
Plot (4,1). From there move up 1, right 2 to (6,2). Draw the line through (4,1) and (6,2).
Why: Slope 1/2 means rise 1, run 2. Starting at (4,1), the next point is (6,2).
Check: Move down 1, left 2 from (4,1) to (2,0); verify (2,0) lies on the line.
Plot y = -x + 3 using any method.
Using intercepts: y-intercept (0,3); x-intercept set y=0 gives x=3, point (3,0). Draw line through (0,3) and (3,0).
Why: Slope is -1, so the line falls from left to right. Intercepts are easy integers.
Check: Check x=1 gives y=2; point (1,2) should lie on the line.
Yes, if the equation is the same and calculations are correct, the plotted line is identical.
Plot it as accurately as possible, or use a table to find integer points nearby for a cleaner line.
Two points determine a line, but plotting a third point helps catch errors.
Yes, but choose values that give easy calculations and include zero and a negative value for a clear pattern.