How to Graph Linear Equations - Y-Intercept Form

Graphing Linear Equations - How it Works - Video

Example 1

Example 1:

We need to graph the equation y = 2x + 3. The first step is to pick 3 small input values or values of x. After you pick the 3 best numbers, usually small numbers since you get will small answers, you substitute the input values to find the values. The reason we need 3 points and not two because, if the line goes through all three points, then we did it correctly. If we do two input values and make a mistake, then we won't know.

The first input value is -1 for y = 2x + 3.

  • y = 2*(-1) + 3 We substitute the value, x = -1.

  • y = -2 + 3 We multiply 2 * -1 ==> -2.

  • y = 1 We add -2 + 3 ==> 1

Now we have the point (-1, 1)

Now we have to do it for the next input value of 0 for y = 2x + 3.

  • y = 2*(0) + 3 We substitute the value, x = 0.

  • y = 0 + 3 We multiply 2 * 0 ==> 0.

  • y = 3 We add 0 + 3 ==> 3.

Now we have the point (0, 3)

Lastly, we have to do it for the next input of 1 for y = 2x + 3.

  • y = 2*(1) + 3 We substitute the value, x = 1.

  • y = 2 + 3 We multiply 2 * 1 ==> 2.

  • y = 5 We add 2 + 3 ==> 5.

Now we have the point (1, 5). We plot the three points and connect them to make a line.

Example 2

Example 2:

We need to graph the equation y = -3x - 2. The first step is to pick 3 small input values or values of x. After you pick the 3 best numbers, usually small numbers since you get will small answers, you substitute the input values to find the values. The reason we need 3 points and not two because, if the line goes through all three points, then we did it correctly. If we do two input values and make a mistake, then we won't know.

The first input value is -1 for y = -3x - 2.

  • y = -3*(-1) - 2 We substitute the value, x = -1.

  • y = 3 - 2 We multiply -3 * -1 ==> 3.

  • y = 1 We subtract 3 - 2 ==> 1

Now we have the point (-1, 1)

Now we have to do it for the next input value of 0 for y = -3x - 2.

  • y = -3*(0) - 2 We substitute the value, x = 0.

  • y = 0 - 2 We multiply -3 * 0 ==> 0.

  • y = -2 We subtract 0 - 2 ==> -2.

Now we have the point (0, -2)

Lastly, we have to do it for the next input of 1 for y = -3x - 2.

  • y = -3*(1) - 2 We substitute the value, x = 1.

  • y = -3 - 2 We multiply -3 * 1 ==> -3.

  • y = -5 We subtract -3 - 2 ==> -5.

Now we have the point (1, -5). We plot the three points and connect them to make a line.

Example 3

Example 3:

We need to graph the equation y = (1/2)x - 4. The first step is to pick 3 small input values or values of x. After you pick the 3 best numbers, usually small numbers since you get will small answers, you substitute the input values to find the values. The reason we need 3 points and not two because, if the line goes through all three points, then we did it correctly. If we do two input values and make a mistake, then we won't know. Now for these input values since we have a fraction, we want to choose multiple of 2s because the fraction will reduce and you will no longer have a fraction.

The first input value is -2 for y = (1/2)x - 4.

  • y = (1/2)*(-2) - 4 We substitute the value, x = -2.

  • y = -1 - 4 We multiply (1/2) * (-2) ==> -1.

  • y = -5 We subtract -1 - 4 ==> -5

Now we have the point (-2, -5)

Now we have to do it for the next input value of 0 for y = (1/2)x - 4.

  • y = (1/2)*(0)- 4 We substitute the value, x = 0.

  • y = 0 - 4 We multiply (1/2) * (0) ==> 0.

  • y = -4 We subtract 0 - 4 ==> -4.

Now we have the point (0, -4)

Lastly, we have to do it for the next input of 2 for y = (1/2)x - 4.

  • y = (1/2)*(2) - 4 We substitute the value, x = 2.

  • y = 1 - 4 We multiply (1/2) * (2) ==> 1.

  • y = -3 We add 1 - 4 ==> -3.

Now we have the point (2, -3). We plot the three points and connect them to make a line.

Example 4

Example 4:

We need to graph the equation y = (-2/5)x - 3. The first step is to pick 3 small input values or values of x. After you pick the 3 best numbers, usually small numbers since you get will small answers, you substitute the input values to find the values. The reason we need 3 points and not two because, if the line goes through all three points, then we did it correctly. If we do two input values and make a mistake, then we won't know. Now for these input values since we have a fraction, we want to choose multiple of 5s because the fraction will reduce and you will no longer have a fraction.

The first input value is -5 for y = (-2/5)x - 3.

  • y = (-2/5)*(-5) - 3 We substitute the value, x = -5.

  • y = 2 - 3 We multiply (-2/5) * (-5) ==> 2.

  • y = -1 We subtract 2 - 3 ==> -1.

Now we have the point (-5, -1)

Now we have to do it for the next input value of 0 for y = (-2/5)x - 3.

  • y = (-2/5)*(0) - 3 We substitute the value, x = 0.

  • y = 0 - 3 We multiply (-2/5) * (0) ==> 0.

  • y = -3 We subtract 0 - 3 ==> -3

Now we have the point (0, -3)

Lastly, we have to do it for the next input of 5 for y = (-2/5)x - 3.

  • y = (-2/5)*(5) - 3 We substitute the value, x = 5.

  • y = -2 - 3 We multiply (-2/5) * (5) ==> -2.

  • y = -5 We subtract -2 - 3 ==> -5

Now we have the point (5, -5). We plot the three points and connect them to make a line.

Live Worksheet 1

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Live Worksheet 2

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