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Understanding y = mx + c

Understanding y = mx + c. What do all the letters mean?. Reviewing graphs. So far we know that the important parts of a line graph are the x-intercept, y - intercept and the gradient, or slope. Graphs. Gradient or slope. X - intercept. Y-intercept. y = mx + c.

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Understanding y = mx + c

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  1. Understanding y = mx +c What do all the letters mean?

  2. Reviewing graphs • So far we know that the important parts of a line graph are the x-intercept, y-intercept and the gradient, or slope.

  3. Graphs Gradient or slope X - intercept Y-intercept

  4. y = mx + c • y = mx + c is the basic rule for any line graph. • The letter m and x represent different aspects that can be read off a graph

  5. What does ‘c’ mean? • ‘c’is the easier of the two letters to work out from a graph. • It is simply the value of the y-intercept. So the point where the graph crosses the y-aixs is the value of c.

  6. Finding ‘c’ Y • Find the value of ‘c’ in the following graphs. 4 3 2 1 -1 -2 -3 -4 -4 -3 -2 -1 1 2 3 4 X

  7. What about ‘m’? • The letter ‘m’ in y =mx + c represents the gradient or slope of a graph. • ‘m’is found by working out the rise of a graph and then the run, or movement across, of the graph. • M = rise run

  8. Finding the Rise 1. Choose a spot on the graph that sits on a value on a y value Y = 2 3 2 1 -1 -2 -3 2. State the y-value of this point Y = 0 3. Choose another point on the graph that sits on a y value -3 -2 -1 1 2 3 4. State the y-value of this point. Rise = 2 – 0 Rise = 2 5. Find the difference between these two points, the rise

  9. Your turn…find the rise IMPORTANT: If a graph slants downwards from left to right, then it is actually a drop rather than a rise and you must put a negative (-) in front. 3 2 1 -1 -2 -3 -3 -2 -1 1 2 3

  10. Finding the run 1. Find the points that you would use for the rise 3 2 1 -1 -2 -3 X = 0 2. Find the x-value of the first point X = -2 3. Find the x-value of the second point -3 -2 -1 1 2 3 4. Find the total movement across, the run Run = -2 to 0 So total movement across is 2 Run = 2

  11. Now find the run… 3 2 1 -1 -2 -3 -3 -2 -1 1 2 3

  12. Putting it together… • Now that you know how to find the rise and the run separately, you need to put the two of them together to find the value of m.

  13. Solving ‘m’… 1. Find the rise Rise = 0 to 3 Rise = 3 3 2 1 -1 -2 -3 Run = -1 to 0 Run = 1 2. Find the run 3. Solve rise run -3 -2 -1 1 2 3 m = rise run m = 3 1 m = 3

  14. Writing the rule… Find the value for c Find the value for m Put the found values into the equation 3 2 1 -1 -2 -3 What is the y-intercept? C = -3 -3 -2 -1 1 2 3 What is the gradient? m = 3 2 Put this into the rule… y = 3x – 3 2

  15. Try it yourself… 3 2 1 -1 -2 -3 3 2 1 -1 -2 -3 -3 -2 -1 1 2 3 -3 -2 -1 1 2 3

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