Linear functions — equation, slope and intercepts
Which equation belongs to the line in the picture?
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The graph of a linear function y = mx + b is a straight line. The number b tells you where the line crosses the y-axis: at the point (0, b). The slope m tells you how much y changes when x grows by 1. If m > 0 the function increases, if m < 0 it decreases. For example, y = 2x − 3 crosses the y-axis at (0, −3) and rises by 2 with every step to the right.
What does this generator do?
On the easy level it draws a line and offers four equations that differ in a sign or swap m and b. On the medium level you get two points and work out m and b. On the hard level the slope is a fraction, for example y = ⅔x − 2, and you find the intercepts and decide whether the function increases or decreases.
How to use it
1) On the graph, find where the line crosses the y-axis — that is b. 2) From there, step to the right and see how much the line rises or falls per step — that is m. 3) From two points: m = (y₂ − y₁) ÷ (x₂ − x₁), then b = y₁ − m · x₁. 4) The x-intercept comes from the equation mx + b = 0.