Question 19328
Hello There:

As far as the -1 goes, there are two ways of looking at it.  It is subtracting a positive 1, or you can say that it is adding a negative 1.

y = 3*x - (+1)

y = 3*x + (-1)

Both interpretations mean the same thing.

I tend to see it as subtracting a positive 1.

To graph the solutions to this equation (a line), we need to find the coordinants of two points that satisfy the equation.  Then it's just a matter of plotting these two points and drawing a straight line through them.

Two easy points to find are the x- and y-intercepts.  The x-intercept occurs when y is zero, and the y-intercept occurs when x is zero.

Let's find the y-intercept first.  Set x equal to zero.

y = 3*(0) - 1

y = -1

The y-intercept is (0, -1)

Now we find the x-intercept.  Set y equal to zero.

0 = 3*x - 1

Add 1 to both sides.

0 + 1 = 3*x + 1 - 1

3*x = 1

Divide both sides by 3.

(3/3)*x = 1/3

x = 1/3

The x-intercept is (1/3, 0).

If you find that these two points are too close together to draw an accurate line for your graph, then you can just pick some values for x and substitute them into the equation to get other solutions.

For example, let's choose 10 for x.

y = 3*(10) - 1

y = 30 - 1

y = 29

So, the point (10, 29) is also a point on the line.

~ Mark