Math Lesson 14.3.4 - Finding the Equation of a Line from a given Graph

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Welcome to our Math lesson on Finding the Equation of a Line from a given Graph, this is the fourth lesson of our suite of math lessons covering the topic of Equation of Linear Graphs, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.

Finding the Equation of a Line from a given Graph

Now, let's suppose that we have no other information except a linear graph and want to know the equation of that line. This should not be a problem given the useful information we can collect from the graph. First, we identify two distinct points with easily identifiable coordinates (it is better to use the intercepts with the axes but this is not always possible); then we find the gradient m. The last step involves the substitution of one of the known points in the equation to find the constant n, as we did in the previous paragraph. Let's consider an example to clarify this point.

Example 5

Find the equation represented graphically by the line below.

Solution 5

First, let's identify two distinct points on the graph. The first is easy, as it represents the y-intercept P(0, 4). Another point with clear coordinates is the point R(4, -6), as shown in the figure below.

We take P as the first point, as it is the leftmost one. Thus, from the formula of gradient m, we have

Now, we substitute the coordinates of any known point (for example P) in the line's equation

to calculate the value of the constant n. Thus, given that x_P = 0 and y_P = 4, we obtain

Therefore, the equation of the line shown in the figure is

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2. Linear Graphs Math tutorial: Equation of Linear Graphs. Read the Equation of Linear Graphs math tutorial and build your math knowledge of Linear Graphs
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4. Linear Graphs Practice Questions: Equation of Linear Graphs. Test and improve your knowledge of Equation of Linear Graphs with example questins and answers
5. Check your calculations for Linear Graphs questions with our excellent Linear Graphs calculators which contain full equations and calculations clearly displayed line by line. See the Linear Graphs Calculators by iCalculator™ below.
6. Continuing learning linear graphs - read our next math tutorial: Parallel, Perpendicular and Intersecting Graphs

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