Question

What is the x-coordinate of the x-intercept of the line that passes through points (-5, 3) and (1, -3)?

Answer 1

You first have to get the equation of the line that passes through these points, using the point-slope form of the equation for a line:\[y - y _{1} = m(x - x _{1})\] where "m" is the slope. But first, you have to get the slope itself with the equation:\[m = \frac{ y _{1} - y _{2} }{ x _{1} - x _{2} }\]where you have points (the given points):\[(x _{1}, y _{1})\]and\[(x _{2}, y _{2})\]

Answer 2

So, start with the slope formula (the second equation). What do you get so far?

Answer 3

I'm so confused!

Answer 4

@nubeer

Answer 5

np. Look at you given points and the format I said they were in. What is x1 and y1? X2 and y2? Hint: you can call either point point 1 and the other point 2. This is the really easy part and it will get you a good start.

Answer 6

The last part of my first post gave you the format so that you can identify x1, y1, x2, and y2. Once you do that, you can substitute those values into the second equation and get "m" which is the slope.

Answer 7

Still having a hard time getting started?

Answer 8

Yes :/

Answer 9

All the points on the line are of the form:

(x, y)

and when we say that you have to specific given points called:\[(x _{1}, y _{1})\]and\[(x _{2}, y _{2})\]all that means is that these are 2 specific points. You are given these points in the problem statement, so all you have to do for the first part is substitute them into the slope formula and do the arithmetic to get the slope which is "m". Try this out and show your work and I'll then be able to see where you are having trouble.

Answer 10

So, start by identifying the points in terms of the x and y subscripted variables. What are x1, y1, x2, and y2? Again, you can call either point point 1 and then the other point is point 2.

Answer 11

Are you familiar with the term "ordered pair"? Do you know what the form:

(x, y)

means?

Answer 12

Are you still there?

Answer 13

yes, I'm frustrated with this.

Answer 14

Don't be afraid to try the work. It's the only way anyone can learn how to do math problems. If I just gave you an answer, which we are not allowed to do, it would not help you in the slightest. So, just give the problem a shot and dive in. Write something down and we'll go from there. You don't want to be stuck just asking for answers because you'll never get out of that rut. I'll help you all I can. I can appreciate your frustration, I really can. There's lots of things I can't do, like draw.

So, if you want to be able to do these things on your own, there's only one way, but I'm aptient and I know I can help, but you'll have to interact.

I'll start the problem out, but in a short while, I'll go back to asking you to give partial answers.

Answer 15

You are given points (-5, 3) and (1, -3). Those are your\[(x _{1}, y _{1}) and (x _{2}, y _{2})\]

Answer 16

okay

Answer 17

So, we can call (-5, 3) point\[(x _{1}, y _{1})\]so x1 = -5 and y1 = 3

Answer 18

okay

Answer 19

Similarly, x2 = 1, and y2 = -3

Answer 20

So, we have these 4 variables (x1, y1, x2, y2) identified. We have an equation for the slope ("m") which is in 5 variables (m, x1, y1, x2, y2), but we know the values of 4 of the variables, so it is really only an equation in 1 variable, "m":\[m = \frac{ y _{1} - y _{2} }{ x _{1} - x _{2} }\]Do you think you are able to make a stab at the substitutions and the solution to "m"?

Answer 21

Hint: wherever you see the variable in that last equation, just put the associated number in its place.

Answer 22

It's 2,3

Answer 23

Making the substitutions,\[m = \frac{ 3 - (-3) }{ -5 - 1 }\]Perhaps you can try to simplify the numerator and the denominator.

Answer 24

Here's something that will give you some visual clues: