How do you graph this equation: |y|+|x-3|+|x-7|=15?

Question

this is a graphing question. what does this equation look like as a graph and how do you graph it. i have graphed it once but i dont think its right. a table of values would be great too.

Sherman 84: What i dont understand is how the graph can be in the negative y quadrants. they are absolute values so would that not suggest that the graph must only be in the positive. That is the main thing that is confusing me. Thanks for the website btw, it'll definitely help in other aspects of math class.

Answer 1

|y| + |x - 3| + |x - 7| = 15

One thing we can do with easy is determine the y-intercept. To do this, we make x = 0. Then

|y| + |0 - 3| + |0 - 7| = 15
|y| + |-3| + |-7| = 15
|y| + 3 + 7 = 15
|y| = 5, which means y = {-5, 5}, and the graph will cross the y-axis at two points.

We can also solve for the x-intercepts. To do this we make y = 0, for |y| + |x - 3| + |x - 7| = 15. Therefore,

0 + |x - 3| + |x - 7| = 15
|x - 3| + |x - 7| = 15

Case 1: (x - 3) >= 0 and (x - 7) >= 0. Then our equation is
x - 3 + x - 7 = 15
2x - 10 = 15
2x = 25, x = 25/2.

{Side note for case 1: if x - 3 >= 0 and x - 7 >= 0, then
x >= 3 and x >= 7, which means x >= 7}

Case 2: (x - 3) >= 0 and (x - 7) < 0. Then our equation is

(x - 3) - (x - 7) = 15, which yields no solution since the x terms cancel out.

Case 3: (x - 3) < 0 and (x - 7) >= 0. Then our equation is

-(x - 3) + (x - 7) = 15, which yields no solution.

Case 4: (x - 3) < 0 and (x - 7) < 0. Then
-(x - 3) - (x - 7) = 15
-x + 3 - x + 7 = 15
-2x + 10 = 15
-2x = 5, so x = -5/2

{Side note: if (x - 3) < 0 and (x - 7) < 0, then x < 3 and x < 7, which implies x < 3.}

We get the two points x = {25/2 , -5/2} as our x-intercepts.

Question still in progress...

What we're going to have are 8 cases, some of which we've already established are not possible.

1) y >= 0, x - 3 >= 0, x - 7 >= 0. Then x >= 7, and
y + x - 3 + x - 7 = 15, so
y + 2x - 10 = 15
y + 2x = 25, so
y = -2x + 25

Graph the line y = -2x + 25 from 7 onward.

2) y >= 0, (x - 3) >= 0, x - 7 < 0. Then 3 <= x < 7, and

y + x - 3 - x - 7 = 15
y - 10 = 15
y = 25

Graph the line y = 25 from 3 <= x < 7.

3) y >= 0, (x - 3) < 0, x - 7 >= 0. It's impossible for all of these conditions to be true, so we reject this possibility (since
x - 3 < 0 implies x < 3, and x - 7 >= 0 implies x >= 7. x cannot be both less than 3 and greater than 7).

Question in progress...

4) y >= 0, (x - 3) < 0, (x - 7) < 0. Then x < 3, and

y - (x - 3) - (x - 7) = 15

y - x + 3 - x + 7 = 15
y - 2x = 5, so
y = 2x + 5. Graph the line y = 2x + 5 for x < 3.

5) y < 0, (x - 3) >= 0, (x - 7) >= 0.

-y + x - 3 + x - 7 = 15
-y + 2x - 10 = 15
-y + 2x = 25
y = 2x - 25

Hmm.. this question has gotten a lot more confusing. I'll stop here.

Answer 2

a million. Take the by-made of the function f(x) = 2x^2 + 3x + a million. 2. you will locate f'(x) = 4x+3. Plug in x=2 to acquire f'(2) = 11. it extremely is your slope. 3. Use the formula y-y_0 = m(x-x_0). here x_0 = 2, y_0 = f(2) = 15 and m = 11 of direction.

Answer 3

|y| + |x - 3| + |x - 7| = 15

if you go to www.quickmath.com, click on Plot under Equations and enlarge it to

-20, 20
-20,20

It looks almost like a parallelogram only with 2 opposite corners cut off.