How am I to find the slope, y-intercept and GRAPH it? PLEASE ANSWER SOON!!! 😬 😬 😬 😬

Question

My teacher showed us that:

if x=1 and y=-1, 0, 1

-1-0-1

1-2 2 My result was undefined.

My question is how are both sides equal? Let's say that x=4 will Y= -4, 0, 4? I don't know how to graph or solve this. What happens when y=-5x or y=x-3? What will X equal then?

X Y X,Y

4 -4 4,-4

4 0 4,0

4 4 4,4

Slope:_____

y- Intercept:______

(What is the way to graph it? up 2 right 1? )

 How is 1/2 equal to both sides?

Answer 1

It took me a few minutes to understand what was going on, but I think I figured it out and can explain.

You see, the normal way you create a linear equation is to use the slope-intercept form:

y = mx + b

That is, for every input, there is a single output--or for every x-value, there is a single y-value. This is not the case here, though. Instead, we have x = 1, and y = -1, 0, AND 1. In other words, we have a multitude of y-values for our x.

Try graphing the three points: (1, -1), (1, 0), and (1, 1). That should give you a visual clue of what's happening.

Do you see it? We have a line going straight up, and straight down. It runs parallel to the y-axis. That's why the answer is undefined--it's never going to cross.

Your other equations, on the other hand, do have answers. To find the y-intercept of those problems, you set x to equal 0 (because that's where the y-axis lies: the point of zero for x), and solve to find its matching coordinate:

y = -5x

y = -5 * 0

y = 0

So the y-intercept would be the point of origin, or (0, 0)

y = x - 3

y = 0 - 3

y = -3

So the y-intercept would be (0, -3)

Go back to that slope-intercept formula, y = mx + b. See b there? That's the y-intercept. That's how the 'intercept' part of the formula gets it's name. So whatever that b-value is, that's what the intercept is going to be so long as you have an actual slope.

y = 5417643258x - 5? y-intercept is -5 because that's the b-value of the equation.

y = x + 444? y-intercept is going to be 444 because that's the b-value of the equation.

y = 10x? y-intercept is going to be 0 because that's the b-value of the equation: nothing.

x = 13? y-intercept is undefind-slash-there is no intercept because it doesn't matter what y is (y can be in essence any and every number), x remains at 13, like your first question had x = 1.

So if you ever need to figure out the y-intercept of any equation built as y = mx + b, just look at the b for your answer.