Turn a rule into a straight line. Change the slope and the start with the buttons, plot points, read equations off lines, solve missions and beat the clock.
Negative numbers: numbers to the left of 0 or below 0 are negative. −3 is smaller than 2. Going left makes x smaller, and going down makes y smaller.
Start here. A rule such as y = x + 2 tells you how to get y from x. Put x = 3 in and you get y = 5. Do that for several x values and you have a table of values. Each pair (x, y) is a point, and the points line up in a straight line.
Plotting points. A point (3, 5) means: go 3 across, then 5 up. The first number is x (across), the second is y (up). Join the points and you have the graph of the rule.
Slope. The slope m tells you how steep the line is: how far it goes UP for each 1 step ACROSS. In y = 2x + 1 the slope is 2, so the line climbs 2 for every 1 across. The slope is rise ÷ run. A flat line has slope 0.
The start. The number c is where the line crosses the y-axis, the upright line where x = 0. In y = 2x + 1 the line starts at y = 1. All together: y = mx + c.
Negative slopes. A line that goes DOWN as you move right has a negative slope, such as y = −2x + 3. Lines can also start below zero, such as y = x − 4, where c = −4.
Parallel lines and points on a line. Lines with the same slope are parallel: they never meet. To test a point, put its x into the rule. If you get its y, the point is on the line. To find the equation from two points, work out rise ÷ run for the slope, then use one point to find c.
It is the rule for a straight line. m is the slope (how steep) and c is where the line crosses the y-axis. For y = 3x + 2, the slope is 3 and the line starts at y = 2.
Pick two points on the line. Count how far you go up (rise) and how far across (run). Divide: rise ÷ run. If the line goes down as you move right, the slope is negative.
The y-intercept is the point where the line crosses the y-axis. It is the value of y when x = 0, and it is the c in y = mx + c.
It means the line goes up half a step for each 1 across, or 1 up for every 2 across. 0.5 is the same as one half.
Just starting: rules, tables and plotting points. I know the basics: slope and the start of the line. Challenge me: negative slopes, parallel lines, points on lines and equations from two points.
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