**plotting points**. You just need to find the points to plot.

**Graph:**3

*x*− 5

*y*= 15

*y*.

To do this, you need to do some algebra. Be careful here, this is where students often make errors.

After isolating the variable

*y*, we now have an equation where

*y*depends on

*x*. That is,

*x*is the

**independent variable**and

*y*is the

**dependent variable**.

**Tip 1**: When solving, be sure to divide BOTH terms on the right side by the coefficient of

*y*. In the example above, we divided −5 into the terms −3

*x*and 15 separately.

Now we have an equivalent equation, which will be easier to work with. Get used to fractions, many equations of lines have fractions in them.

**Graph:**

*y*= 3/5

*x*− 3

*x*-values and then substitute them into the equation to find the corresponding

*y*-values.

**Tip 2:**Choose some negative

*x*-values, zero, and some positive

*x*-values.

**Tip 3**: Avoid fractions by choosing

*x*-values wisely.

Since the denominator of 3/5 is 5, we will choose multiples of 5 to avoid fractions. In this case, we choose −5, 0, 5, 10, and 15 for the

*x*-values. Make a table,

Then substitute these

*x*-values into the equation to find the corresponding

*y*-values.

The table gives us 5 ordered pairs to plot. Since

*x*-values here are multiples of 5, we choose the tick on the

*x*-axis to represent 5 units. Similarly because the

*y*-values are multiples of 3, we will choose a scale of 3 units on the

*y*-axis.

**Tip 4**: Impress your teacher by placing an arrow on either end of the line to indicate that it continues forever.

That’s it! The general steps are outlined below.

**Step 1:**Solve for

*y*so that your equation looks like

*y*=

*mx*+

*b*.

**Step 2:**Choose any five

*x-*values. (You only really need two.)

**Step 3:**Plug in to find the corresponding

*y*-values.

**Step 4:**Plot the points and connect them with a straightedge.

Here is another example.

**Graph:**−2

*x*− 3

*y*= 6

*y*.

**Tip 5:**Avoid the following common error of dividing only one term.

When dividing a binomial by a number you must divide both terms by that number. Next, choose some

*x*-values. Avoid fractions here by choosing −6, −3, 0, 3, and 6. Substituting we have,

And plotting these points we have the graph of

*y*= −2/3

*x*− 2,

Some more examples follow.

**Graph:**

*y*= 2

*x*− 4 by plotting five points.

**Graph:**

*y*= −

*x*− 2 by plotting five points.

Choosing a scale when creating a blank coordinate system will take some thought. Keep in mind that the scale on the

*x*-axis need not be the same as the scale on the y-axis.

**Graph:**

*y*= 1/2

*x*− 6 by plotting five points.

When the coefficient of

*x*is a fraction, choose

*x*-values to be multiples of the denominator so that you might avoid unnecessarily tedious calculations.

**Graph:**

*y*= −3/2

*x*+ 6 by plotting five points.

But wait there’s more. In the next method [ Plot Using Intercepts ] coming soon, we show an easy two point method for graphing lines. Read on!

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