graph the equation

Question

Graph y+2=1/3(x+6)

SHOW WORK

Answer 1

This equation is in point-slope form: y - y₁=m (x - x₁) where (x_1, y₁) and m are all (not so) hidden in the equation.

 

By just looking that the equation, we see that the m (or slope) is 1/3. Recall slope means rise/run...so when we are ready to graph we will rise 1 and run 3 based on the slope in the equation.

 

You will notice the equation we were given has plus/positive signs rather than negative signs in the general formula.

 

We can re-write the given equation to match the point-slope formula like this:

     y-(-2)=1/3(x-(-6))...which matches our formula perfectly!

 

THEREFORE, (-6, -2) is a point on the line. Plot that point on your coordinate graph, then from there follow the slope rule given to us (rise 1, run 3) for your second point. Connect the points to create your line and you are DONE! : )

Answer 2

Hi Quinton, 

 

To graph this line, I suggest you first convert the equation to slope intercept form, which looks like this:  y=mx+b

 

to do this, start with your equation:

 

y+2=1/3(x+6)

 

Then multiply 1/3 through the right hand side using the distributive property:

 

y+2 = 1/3 x + 2

 

Then subtract 2 from both sides to get:

 

y = 1/3 x

 

So, the slope of the line is 1/3 and the y intercept is 0

 

To graph the line, start from point (0,0)  - that's the y intercept - and from that point, go up 1 unit and then go to the right 3 units.  (That's because a "rise" of 1 and a "run" of 3 is equal to the slope of 1/3.)  The point that you land on will be (3, 1).  Draw a line that goes from (0,0) through (3,1) and this will be the answer to your problem.

 

I cannot draw this for you on the wyzant site, so I hope this is helpful to you!

 

Jeff

 

Answer 3

always get y by itself.

 

I'm assuming the (x+6) is multiplied by the fraction 1/3. If the (x+6) is in the denominator the problem is very different!

y+2=(x+6)/3

distribute the 1/3: y+2=x/3 + 2

subtract 2 from each side:  y=x/3

 

This is a straight line with y-intercept at (0,0) and x-intercept at (0,0); and slope = +1/3.

That is, the line rises 1 unit for every three it goes to the right.  One point on this line is (3,1), for example.