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Learn to plot y = mx + b by choosing slope and intercept values, predicting the line, then checking it on a coordinate grid.
A line written as y = mx + b is controlled by two numbers. The slope m tells how steep the line is and which way it runs. The intercept b tells where the line crosses the vertical axis. In this lesson you will predict a line from m and b, sketch it on a grid, and then verify the sketch by checking points. The planned slope graph maker uses two sliders, one for m and one for b, with a live equation display. Before adjusting any slider, you will write a prediction so that the tool confirms your reasoning rather than replacing it.
Practice materials: Printable downloads are not available for this lesson yet. Use the instructions and four exercises below.
Start with the equation in the form y = mx + b. The value b is the y-intercept: the point (0, b) is always on the line. The value m is the slope: from any point on the line, moving 1 unit right changes y by m units. A positive m rises to the right; a negative m falls to the right; m = 0 gives a horizontal line.
Use a consistent unit on both axes. If each grid square represents 1 unit horizontally and 1 unit vertically, then a slope of 2 means up 2 squares for every 1 square right. If the axes use different scales, convert before counting squares.
A slider is useful only after you commit to a prediction. For each task, record the predicted intercept, the predicted direction, and one predicted point other than the intercept. Then adjust m and b to match the equation and compare the displayed line with your prediction.
Record three observations for each line: whether the line rises or falls, where it crosses the vertical axis, and whether a chosen test point lies on it. These observations turn a visual check into a written record.
A line is correct when every point on it satisfies the equation. Choose two x-values, compute y = mx + b for each, and confirm that both points lie on the drawn line. If one point is off, recheck the slope count and the intercept.
Keep units consistent. If the grid uses 1 unit per square, state that in your work. If a hypothetical example uses 2 units per square, label it clearly as a chosen scale, not a standard.
Plot y = 2x + 1 on a grid where each square is 1 unit. Predict the intercept, direction, and one extra point before drawing.
The intercept is (0, 1). The slope 2 is positive, so the line rises. From (0, 1), move 1 right and 2 up to reach (1, 3). A check point at x = 2 gives y = 2(2) + 1 = 5, so (2, 5) lies on the line. The line passes through (0, 1), (1, 3), and (2, 5).
Plot y = 3x - 2 on a grid with 1 unit per square. State the intercept, direction, and one extra point.
Intercept (0, -2); slope 3 is positive so the line rises; extra point at x = 1 gives y = 1, so (1, 1) is on the line.
Why: b = -2 places the intercept below the origin. m = 3 means up 3 for every 1 right. Substituting x = 1 gives y = 3(1) - 2 = 1.
Check: Substitute x = 2: y = 3(2) - 2 = 4, so (2, 4) should also lie on the drawn line.
Plot y = -1x + 4 on a grid with 1 unit per square. State the intercept, direction, and one extra point.
Intercept (0, 4); slope -1 is negative so the line falls; extra point at x = 2 gives y = 2, so (2, 2) is on the line.
Why: b = 4 places the intercept above the origin. m = -1 means down 1 for every 1 right. Substituting x = 2 gives y = -2 + 4 = 2.
Check: Substitute x = 1: y = -1 + 4 = 3, so (1, 3) should lie on the line.
Plot y = 0x + 3 on a grid with 1 unit per square. Describe the line and give two points on it.
The line is horizontal through (0, 3). Points include (0, 3) and (2, 3).
Why: m = 0 means no vertical change as x increases, so y stays at 3 for every x.
Check: Substitute x = 5: y = 0(5) + 3 = 3, so (5, 3) should lie on the line.
A grid uses 2 units per square on both axes. Plot y = 1x + 2. State how many squares right and up to move from the intercept, and give one extra point in grid units.
Intercept at (0, 2), which is 1 square up. Slope 1 means 1 unit up per 1 unit right, which is half a square up per half a square right; equivalently, move 1 square right and 1 square up to reach (2, 4). Extra point (2, 4).
Why: Because each square is 2 units, a slope of 1 corresponds to equal vertical and horizontal unit changes. Moving 1 square right changes x by 2 and y by 2, matching slope 1.
Check: Substitute x = 4: y = 4 + 2 = 6, so (4, 6) is 2 squares right and 3 squares up from the origin; confirm it lies on the line.
m controls steepness and direction. Larger positive values are steeper upward; negative values fall to the right.
b is the y-intercept, the y-value where the line crosses the vertical axis at x = 0.
Yes. When m = 0, the equation becomes y = b, a horizontal line through (0, b).
Substitute two x-values into the equation, compute y, and confirm both points lie on the line.