کارهایی که یادگیرنده بعد از این درس می‌تواند انجام دهد
- Explain that changing m in y = mx + c alters the steepness and direction of the line
- Identify the y-intercept of a line from its equation and from its graph
- Determine whether a given equation will produce a straight line or a curve
۱ · بخوان
Your taxi rule made a table and a graph: it started at £2 and rose £1.50 a mile. A rule like that has a name. It is a linear function, written y = mx + c, and every equation written this way makes a straight line when you graph it. The number m is the gradient. It tells you how steep the line is and whether it slopes up or down as x increases. The number c is the y-intercept. It tells you where the line crosses the y-axis, the point where x = 0.
Take y = 2x + 3. Here m = 2 and c = 3. The line crosses the y-axis at 3, and for every step you move right, it climbs up by 2. You could sketch this line just from the equation: start at 3 on the y-axis, then go up 2 and right 1, again and again.
Not every equation makes a straight line. If x is squared, like in y = x² + 1, or if x is under a fraction, like y = 1/x, the graph curves instead. A straight line happens when x is on its own, to the power 1, or when there is no x at all, as in y = 3.
y = mx + c always draws a straight line, where m sets the steepness and direction, and c sets the y-intercept.
The rewritten readings were written for this dataset.
۲ · ببین
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