# How to Graph Linear Equations - Standard Form

## Graphing Standard Equations - How it Works - Video

### Example 1

Example 1:

To graph a linear equation that is in standard form, one way is to substitute the number, 0, in for x and for y.

Let's substitute 0 in for x.

• 5(0) + 2y = 10

• 0 + 2y = 10 5 * 0 = 0

• 2y = 10 Adding zero doesn't affect it so we can drop it.

• y = 5 Now we have to do an inverse step by dividing both sides by 2.

So our point is (0, 5) and then we plot the point on the graph.

Next we substitute 0 for variable, y.

• 5x + 2(0) = 10

• 5x + 0 = 10 2 * 0 = 0

• 5x = 10 Adding zero doesn't affect it so we can drop it.

• x = 2 Now we have to do an inverse step by dividing both sides by 5.

So our point is (2, 0) and then plot the point on the graph. Finally we connect the points by drawing a line.

### Example 2

Example 2:

To graph a linear equation that is in standard form, one way is to substitute the number, 0, in for x and for y.

Let's substitute 0 in for x.

• 2(0) - 3y = 6

• 0 - 3y = 6 2 * 0 = 0

• -3y = 6 Adding zero doesn't affect it so we can drop it.

• y = -2 Now we have to do an inverse step by dividing both sides by 5.

So our point is (0, -2) and then plot the point on the graph.

Next we substitute 0 for variable, y.

• 2x + 3(0) = 6

• 2x + 0 = 6 2 * 0 = 0

• 2x = 6 Adding zero doesn't affect it so we can drop it.

• x = 3 Now we have to do an inverse step by dividing both sides by 2.

So our point is (3, 0) and then plot the point on the graph. Finally we connect the points by drawing a line.

### Example 3

Example 3:

To graph a linear equation that is in standard form, one way is solve for y and use the slope and the y-intercept to graph the equation.

We have 3x + 2y = 8

• 2y = -3x + 8 In this case, our first step is do an inverse step by subtracting -3x from both sides.

• y = (-3/2)x + 4 Now we have to do one more inverse step and divide both sides by 2

Now we use the y-intercept to plot the first point, (0, 4) and then use the slope to find the next. Since the slope is negative, the line is going to go down and to the right. Remember it is rise (horizontal) over run (vertical). So now we use the slope, -3/2, to draw the next point.

So now we go 2 spaces to the right and 3 spaces down to go to (2, 1). Now we have two points. Let's do it more one time to go to (4, -2). Finally we connect all the points by drawing a line.

### Example 4

Example 4:

To graph a linear equation that is in standard form, one way is solve for y and use the slope and the y-intercept to graph the equation.

We have 8x - 4y = 12

• -4y = -8x + 12 In this case, our first step is do an inverse step by subtracting -8x from both sides.

• y = +2x - 3 Now we have to do one more inverse step and divide both sides by -4.

Now we use the y-intercept to plot the first point, (0, -3) and then use the slope to find the next. Since the slope is positive, the line is going to go up and to the right. Remember it is rise (horizontal) over run (vertical). Now we use the slope, 2 or 2/1, to draw the next point.

So now we go 2 spaces up and 1 space to the right to go to (1, -1). Now we have two points. Let's do it more one time to go to (2, 1).