How do you graph y=3x+2? please list all steps?

Question

How do you graph y=3x+2? please list all steps?

Answer 1

Pick a few numbers at random for x or y, and find the other:

First, I'll pick 0 for x.  If x is 0, then y = 2.  Plot (0, 2) on the grid.

Now, I'll pick 5 for x.  No reason I chose 5, I just did.  If x is 5, then y is 17.  Plot (5, 17) on the grid.

I've done this enough times to know just by looking at the equation that you can stop after these two points and just draw a line through them, and continue that straight line in both directions.  If the x were squared or cubed or something, it would make a curve instead of a straight line, so you'd have to pick several more points.

Answer 2

This equation is modeled after y = mx + b, where m = the slope and b = the y-intercept, so you already know one point - (0,2) (the y-intercept). Then you can just plug in x-coordinates to find out y.

Example

x = 1, y = 3(1) +2, so y = 5

(1, 5)

x =2, y = 3(2) +2, so y = 8

(2,8)

And so on...

Answer 3

The equation is in slope-intercept form.

The coefficient of x is the slope of the line. Since it's 3, the line rises 3 units of y for each 1 unit increase in x.

The constant value of 2 indicates where the line passes through the y-axis. (This is known as the y-intercept.) Figuring the y-intercept is done by setting x equal to 0. This gives you y = 2 at x = 0.

So the line passes through point (0, 2) and rises 3 units for each 1 unit increase in x. The next point on the line moving to the right along the x-axis is the point (1, 5) with each following point being 3 units higher in its y value.