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When we have an equation with two different unknowns, like y = 2x + 1, we cannot solve the equation.

We can instead find pairs of x and y values that make the left side equal the right side

We can use a table of values to show the number pairs:

To complete this table of values, for y = 2x + 1, we need to find out the value of y when x = 0, when x = 1, when x = 2 and when x = 3

We do this using substitution

We can use these values to complete the table
Example 1: Complete the table of values for x + y = 6
We can find the y values using substitution:

We can now complete the table:
Example 2: Complete the table of values for y = 3x - 5
In this example we have negative x values in the table. It is often easier to start with the positive x values:

We can notice a pattern in these y values, they are going up by 3 each time (from left to right or down by 3 each time from right to left).

We can expect that for x = -1, y = -8
When x = -2, y = -11
and when x = -3, y = -14

Substituting gives:

If we make a mistake in our calculations we will be able to notice as our values would not fit the pattern.
Try these:
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We can use a table of values to draw a graph. Each pair of values become a set of coordinates (x,y).
Example: Here is the table of values for y = 2x - 3
draw the graph for y = 2x - 3
On a graph we will plot the coordinates:
(-3,-9), (-2,-7), (-1,-5), (0,-3), (1,-1), (2,1) and (3,3)

We join the points up with a straight line.
Example: Draw the graph for y = 3x + 1
Here we have not been given a table of values.

We can create a table of values. We can see that the x values on the graph are -2, -1, 0, 1 and 2. We can use these for our table of values:

We can now complete our table bu substituting our x values into the equation:

We can use these values to complete the table

The next step is to plot the coordinates:
(-2,-5), (-1,-2), (0,1), (1,4) and (2,7)

And finally we use a ruler to draw the line

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Maths revision video and notes on the topic of drawing straight line graphs.

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Maths Genie - Revision - Finding (or Estimating) the Mean from a Frequency Table

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Maths revision video and notes on the topic of finding or estimating the mean from a given frequency table.

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Maths revision video and notes on the topic of upper and lower bounds.

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Maths Genie - Revision - Angles in Parallel Lines

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Maths revision video and notes on the topic of Angles in Parallel Lines.

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Maths Genie - Revision - Trigonometry (SOHCAHTOA)

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Maths revision video and notes on the topic of finding missing angles and lengths in right angled triangles using the trigonometric ratios sine, cosine and tangent.

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Maths Genie - Revision - Compound Interest and Depreciation

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Maths revision video and notes on the topic of Compound Interest and Depreciation.

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Maths Genie - Revision - Similar Shapes (Area and Volume)

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Maths revision video and notes on the topic of similar shapes, including harder problems which relate to area and volume.

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Maths Genie - Revision - Compound Measures

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Maths revision video and notes on the topic of solving problems involving the compound measures of speed, density and pressure.

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Maths revision video and notes on the topic of Bearings.

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The Corbettmaths Practice Questions on Area Under a Graph

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Maths Genie - Revision - Cumulative Frequency

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Maths revision video and notes on the topic of Cumulative Frequency.

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Maths Genie - Revision - Velocity Time Graphs

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Maths revision video and notes on the topic of velocity time graphs.

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Maths Genie - Revision - Simultaneous Equations

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Maths revision video and notes on the topic solving simultaneous equations.

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Maths revision video and notes on the topic of Histograms.

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Maths Genie - Revision - Angles in Parallel Lines

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Maths revision video and notes on the topic of Angles in Parallel Lines.

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Maths Genie - Revision - Finding (or Estimating) the Mean from a Frequency Table

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Maths revision video and notes on the topic of finding or estimating the mean from a given frequency table.

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Maths Genie - Revision - The Equation of a Line

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Maths revision video and notes on the topic of the equation of a line, y=mx+c.

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Maths Genie - Revision - Finding the gradient of a straight line

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Maths revision video and notes on the topic of finding the gradient of a linear graph or line segment.

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Maths Genie - Revision - Factorising Quadratics with a Coefficient of x^2 greater than 1

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Maths revision video and notes on the topic of factorising quadratics with a coefficient of x squared greater than one.

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Maths Genie - Revision - Algebraic Proof

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Maths revision video and notes on the topic of algebraic proof.