Graphs

  • Created by: Cat91
  • Created on: 07-05-18 12:16

Coordinates

  • Coordinates can be used to describe the positions of points on a grid.
  • The horizontal axis is labelled x. The verticle axis is labelled y. 
  • You always put the x axis first and write it in bracets, e.g (9,1)
  • Sometimes theres negative number, if it's the first number then it's because the point is on the left side of the 0. If it's the second number it's because the point is underneath the 0.
  • The point (0,0) is known as the 'origin'.

Midpoints:

  • Straight lines have a line segment, which is a short part of it.
  • Exactly in the middle of a line is called the midpoint.
  • If you know the coordinates of the ends of the line you can find the midpoint.
  • If you add the x-coordinates and divide by 2, the do the same to the y, then put the results together to get the midpoint.
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Gradients of straight lines

If you want to know the steepness of a line, find the gradient. You can work it out using the rule: Gradient = distance up/distance across.You need to draw a triangle to work out the gradient. Write the distance up and the distance across. Make sure you get the scale right. 

Triangle tips:

  • To be less likely to make mistakes draw one side of your your triangle on a large grid line.
  • Your calculations will be more accurate if you use a larger triangle.
  • Use the scale to work out the distances up and across. Don't just count the squares.
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Straight line graphs

The equation for straight line graphs is y=mx+c. The m is the gradient. The c is the y-intercept. Using a a table of values can help make it easier to plot the graph.

Finding equations can be done with a graph and looking at the y-intercept. Use a gradient triangle to find the gradient. Put the gradient and the y-intercept into the equation. If an equation is in a different order, you can rearrange it. 

When you are given one or two points, you can use algebra to figure out the equation. 

1 point:

  • Put the gradient into the equation.
  • Put in the x and y values from the point.
  • Solve the equation.

2 points:

  • Draw a sketch showing the two points.
  • Work out the gradient using the triangle.
  • Use the method for 1 point to solve it.
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Parallel lines

Parallel lines have the same gradient.

Parallel lines never meet.

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Real-life graphs

These are really hard to explain without a graph, so I'm going to skip it. If you need to know stuff about this then find an example with a graph (https://www.bbc.com/education/guides/zpmfgdm/revision).

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Distance-time graphs

A distance-time graph shows how distance changes with time. A horizontal line means no movement. Straight lines means moving at a constant speed. The gradient shows the speed. When the graph stops increasing and starts decreasing, it shows that it is turning around. (Sorry, not easy to explain without examples, try https://www.bbc.com/education/guides/zpmfgdm/revision/2).

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