Straight-line graphs. What the numbers in a rule do to its line, solving equations with graphs, and modelling with lines.
From a growing pattern or a rule to a table of values, a graph, and what a graph of real data says.
In a growing pattern, look at what each new figure adds. That gives a rule, and the rule gives any figure without drawing it.
A rule turns each input x into an output y. Choose inputs, work out each output, and write them as a table of ordered pairs (x, y), input first.
Plot each ordered pair from a rule's table as a point, across first and then up. For a rule like y = 2x + 1, the points lie on a straight line.
A point on a graph of real data pairs two measurements. Find one value on its axis, go to the line, and read across to the other axis.
Describe how one measurement changes as the other increases, one section of the graph at a time: it increases, decreases or stays constant.
To see what one variable does to a formula, change only that one and hold the rest still. Doubling h in V = lwh doubles V; doubling the side of a square makes its area four times as big.
What m and c do to the line y = mx + c.
In y = mx + c, the number in front of x sets how steep the line is and which way it goes.
In y = mx + c, the number on its own moves the line up or down without changing its steepness, so lines with the same m are parallel.
y = 2x + 1 is a line; y < 2x + 1 is every point below it. Draw the boundary (dashed if points on it are not included, solid if they are), then test a point to see which side to shade. Vertical lines are x = a; horizontal lines are y = a.
Solve equations where two lines meet, then model real situations with lines.
Draw each side of an equation as a line. Where the lines meet, both sides are equal, so the x there is the solution.
Many real costs and amounts are a starting amount plus a rate. The starting amount is c and the rate is m, so the rule is y = mx + c.
Put two rules on one graph. Where the lines cross they cost the same; on either side, the lower line is the cheaper plan. Then check where the model makes sense.
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