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A Couple of Points on Straight Line Graphs...

  • Jul 1, 2022
  • 2 min read

Here we look at a great way to construct/sketch a straight line graph that requires just two points.


The two-point gradient and y-intercept method


The equation for a straight line is

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Where x and y are variables that relate to the x and y axes of a graph.

The gradient (slope) of the line is given by m - this is the number immediately before the x (it's known as the coefficient). If the coefficient is a negative value, the gradient will slope downwards on a graph.


The c term is the y-intercept - the point on the y-axis where the line will cross.

Look at the following equation...

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If it can be manipulated so that it has the form y = mx + c, it can be graphed.

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In this case, the line will have a gradient of 3 and will cross the y-axis at y = 4.

The line can be graphed quickly by plotting just two points.


The easiest point to plot is the y-intercept. This occurs when x = 0 so the coordinates will be (0, 4)

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The y-intercept

Another point on the graph is needed and it can be found using the value for the gradient, 3.


The gradient is usually found by calculating...

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...the change in y divided by the change in x for 2 points on a line.


Looking at the equation, this is already done. The value 3 can be represented as .

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This just means that for every unit increase in a value for x, there will be 3-fold unit increase in the value of y.


Starting with the y-intercept coordinate, move 1 place along the x-axis and 3 places up the y-axis, to get a second coordinate as follows:


The x value will move from 0 to 1 and the y value will move from 4 to 7 (increasing by 3). The new coordinate will be (1, 7).

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Graph showing two coordinates

Complete by lining up a straight edge to the two coordinates and pencil in the line. This line represents the equation and can be read off to find the corresponding values for the variables x and y.


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Graph of y = 3x + 4

The x-intercept

The point where the line crosses the x-axis can also be found from the equation...

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Set the y value to 0 (the value for y when the value for x lies directly on the x-axis)...

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Make x the subject...

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Summary

  • Find and plot the y-intercept from the equation for a straight line

  • Use the coefficient of x to find a second point on the graph

  • Line up the points and draw a straight line!



Have a go at plotting the following. You can construct your own graphs or use the Graphing Blank provided below.

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Graph paper

Here are the solutions

Comments & likes always welcome!


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