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Welcome to a new lesson. After mastering on how to read and write coordinates, we can now use it to visualize the graph a linear equation.

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Let's say you are given the equation y = 2x + 1. This equation, by itself, may not makes much sense.

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But if we were to use the Coordinate plane to plot a graph of this equation, you get to actually see how this equation looks like.

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To do so, first, you have to draw out a table like this. This table is useful to store the coordinates of the point that you are going to calculate soon.

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Now, let the variable x to take up the first row of this table.

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Similarly, let the variable y take up the second row. With this, you can see that, these empty column here will used to store coordinates of one point.

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Now let's start filling this table. Let me put the value, 1 in the box right here. By doing so, you will have a point on the plane with it's x-coordinate = 1.

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But you have a problem. Though you have the x-coordinate as 1, you still do not know what is the y coordinate.

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This is where you will have to use this equation, to find out the y coordinate of this point when x = 1.

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Now, substitute x=1 right here, solve for y by first multiplying 2 with 1. You will get 2. 2 plus 1 gives you 3. Let's put this new value y = 3 into the table.

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It now means that, when this point's x coordinate = 1, the value of y coordinate for this equation is 3.

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With this newly calculated point, let us now adjust this point to the correct coordinates (1,3).

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Alright, you now have your first point from y = 2x + 1.

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To continue further, we will do the same thing for x = 2, x = 3 and x = 4.

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For x =2 , we will now solve this equation. Substitute x=2. multiply 2 with 2 gives 4 .Add 4 with 1. You will get y = 5. Let's put this value into the table. Now, you have a new coordinates (2,5).

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This point is located right over here.

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For x =3 , we will now solve this equation. Substitute x =3..Multiply 2 with 3 gives 6. Add 6 with 1. You'll get y = 7. Let's put this value into the table. Now, you have a new coordinates (3,7).

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This point is located right over here.

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For x =4 , we will now solve this equation. Substitute x =4. Multiply 2 with 4 gives 8. Add 8 with 1. You'll get y = 9. Let's put this value into the table. Now, you have a new coordinates (4,9).

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This point is located right over here.

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You see that these points forms a pattern here.

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Now, when we connect these points together, we will get a straight line. This line is the graph of y = 2x + 1.

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So, what you have learn showed you how draw the graph of a linear equation.

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Alright, that is all for this lesson. You can move on to the practice questions to test your understanding.