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Co-ordinates: To find the co-ordinates of a graph the axis have to be identified. The vertical axis is known as the 'y' axis, and the horizontal axis is known as the 'x' axis. The position of a point on a
graph is defined by its 'x' co-ordinate first, and its 'y' co-ordinate second. The point A is at x = 3, and y = 2, or A(3,2). When there are more than one point on a graph they are connected by a straight line or a curved line.
Example: A Farenheit to Centigrade chart. The formula for conversion is F = C x
+32. If a few conversions are made the rest will be found after the straight line has been drawn.
When C = 0, F = 32. When C = 20, F = 68. When C = 35, F = 95.
First point: (32, 0), Second point: (68, 20), Third point (95, 35).
On completion of the chart it is possible to find other conversions simply by reading any value of C. Follow the reading to the sloping straight line. Where it hits the line read down for the corresponding value in F, ie 10C = 50F.
Lines and Gradients: The gradient of a line is its ratio of its 'y' axis change to its 'x' axis change. On a straight line graph this is quite simple, just find two points on the slope, measure the distance on the 'x' axis, then measure the distance on the 'y' axis. Divide the 'y' axis measurement by the 'x' axis measurement for the gradient.
Example: Looking at the temperature chart there are readings at 20
C and at 35
27 = 0
556 and its positive as it travels left to right uphill. A slope travelling downhill would be negative.
To find the gradient on a curved line it is necessary to take the reading at a given point on the line. At this point a tangent is drawn and then two points can be taken as the method for the straight line.
Example: Find the gradient of the curve at (3, 3
Draw a tangent from the curve at the point, complete the triangle. Take the measurements on the 'y' axis and on the 'x' axis. Change in Y is 4, change in X is 4
1. The horizontal line bold, shows Y = 6. There are no X co-ordinates.
2. The Vertical line bold, shows X = 4. There are no Y co-ordinates.
3. The diagonal line travels uphill from left to right and is Y = X. The slope is 1, for each increased Y measurement it also increased in X measurement.
4. The diagonal line travels downhill from left to right and is Y = -X. The slope is -1.
Sloping Lines through the Origin: The origin is the zero on the 'x' axis and the zero on the 'y' axis. The equation for a sloping line through the origin is y = mx for uphill and y = -mx for downhill. The 'm' stands for the gradient of the slope, the greater the number the steeper the slope. For the graphs shown above Fig 3. equation is: y = 1x, and for Fig 4. equation is: y = -1x.
Other Sloping Lines: Sloping lines that do not pass through the origin but cross the 'y' axis
elsewhere have an equation: y = mx + c. The 'm' being the gradient, the 'c' being the value of the crossing of the 'y' axis.
Fig 5. The slope 'm' is 2, (Y: 8 - 4 = 4, X: 6 - 4 = 2), the crossing point 'c' is -4 on the 'y' axis. The equation is: y = 2x -4.
Graphs can be drawn from an equation. If the equation is mixed up ie. 4 = 2x - y, rearrange it to its standard form. Mark the crossing point and calculate the gradient, ie. 2 is two up (Y) to one across (X). Place a second marker and draw in the straight line.
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