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📈 Graphing Equations

See how linear equations draw straight lines — and what slope and y-intercept really mean — then meet the U-shaped curves that quadratics make.

3
lessons
~30 min
to learn
🔢 Math
subject
Teens
level
Start the course →

What you’ll learn

  1. Lines From EquationsUnderstand y = mx + c, and interpret the gradient m and y-intercept c from an equation and a graph.A linear equation always graphs as a straight line, written y = mx + c. The gradient m sets the steepness and direction — bigger is steeper, negative goes downhill — while c is the y-intercept, where the line crosses the vertical axis at (0, c). Reading m and c lets you picture a line before plotting a single point.
  2. Plotting LinesPlot linear graphs from a table, rearrange equations into y = mx + c, and find gradients from two points.To plot a line, build a table of x-values and compute each y, then join the points. Equations not in y = mx + c form can be rearranged to reveal their gradient and intercept, and the gradient between two points is rise ÷ run — the change in y divided by the change in x.
  3. Curves From SquaresRecognise that quadratics graph as parabolas, explain why, and plot a simple quadratic from a table.A quadratic equation contains x² and graphs as a U-shaped curve called a parabola. Because squaring makes negatives positive, points equally far from the middle share the same height, folding the graph into a symmetric curve. If the highest power of x is 1 the graph is a straight line; any x² term makes it a curve.

Questions this course answers

In y = mx + c, what does m represent?

m is the gradient — how steep the line is and which way it tilts.

Where does the line y = 2x + 3 cross the y-axis?

The y-intercept is c, which is 3, so it crosses at (0, 3).

What happens to the line if you increase m in y = mx + c?

A larger gradient makes the line steeper.

Rearrange 2x + 3y = 12 into the form y = mx + c.

Subtract 2x then divide by 3: y = 4 − (2/3)x.

A line passes through (0, 1) and (2, 5). What is its gradient?

Rise 4 over run 2 gives a gradient of 2.

What shape does the graph of a quadratic like y = x² − 4 make?

Quadratics graph as parabolas — smooth U-shaped curves.

Grounded in trusted sources

  • Khan Academy
  • OpenStax
  • National Council of Teachers of Mathematics (NCTM)
  • BBC Bitesize — Maths

Every Wunder lesson is built from real, reputable sources — never invented.

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