How do I graph an equation of a line?

Question

I have to graph an equation of a line in y=mx+b

For example, the first one I have to graph is y=2x+7 but I'm not sure how to graph that?

Can someone please help explain the process? Thank you!

Answer 1

Two points determine a line.  We represent points like this:   (x,y)

 

So, let's find two points that make the equation y=2x+7 true.

   Let x=0.   This gives the point   (0,7)

   Let x=1.   Evaluate the formula.  This gives the point   (1.9)

 

Now, draw a long line through BOTH points.  This is the line defined by the equation y=2x+7.

 

For other lines in slope-intercept form (y=mx+b), it is pretty to let x=0 for one point.  Then pick another value for x (like x=1) and calculate the y value of that point.  That's it. Draw the line.

Answer 2

To graph this line, we need to know the slope the y-intercept.  The slope is m and the y-intercept is b.  Knowing that,

 

m = 2

b = 7

 

 

The slope is the distance in y over the distance in x between two points.  The y-intercept is the point on the y-axis.

 

First, we can plot the y-intercept on a coordinate system.  The y-intercept is (0, 7).  From there, we can use the slope to plot the next point.  Since the slope is positive, the next point going in the rightward direction will be somewhere above the first point.

 

From the first point, which is the y-intercept, move one unit to the right and 2 units up.   The next point will be (1, 9).

 

These are your two points: 

 

(0, 7) and (1, 9)

 

 

Connect these two points throughout the coordinate system to get your line.