Algebra- Graphing

[Imma.Potato]

Suppose that y = 2x - 3 The following points lie on the graph of this equation.
A(a, 2a-3) B(b, 2b-3) C(c, 2c-3)

Fita claims that the slopes AB, BC, and AC are equal. Prove that Fita’s claim is correct. Show your work and explain your reasoning.

 

[mmm4444bot]

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Hello. Please share what you've tried or thought about, thus far. Thank you.

Fita's claim is obviously true, from the definition of a straight line (the slope has to be the same from point to point).

First, what is the slope of the line? We can answer that without calculations, by looking at the given equation.

Next, what happens when you put the (x,y) coordinates given for points A and B into the slope formula and simplify?

?

 

[Imma.Potato]

Posting Guidelines (Summary)

Welcome to our tutoring boards! :) This page summarizes the main points from our posting guidelines. As our name implies, we provide math help (primarily to students with homework). We do not generally post immediate answers or step-by-step solutions. We don't do your homework. We prefer to...

www.freemathhelp.com

Hello. Please share what you've tried or thought about, thus far. Thank you.

Fita's claim is obviously true, from the definition of a straight line (the slope has to be the same from point to point).

First, what is the slope of the line? We can answer that without calculations, by looking at the given equation.

Next, what happens when you put the (x,y) coordinates given for points A and B into the slope formula and simplify?

?

I honestly don’t get what u said in the last part but this is what I got so far
y= 2x -3 : -3 is the y intercept and 2x=2/1 which is the slope
When I go to the A(a, 2a-3) B(b, 2b-3) C(c, 2c-3)
The letters inside the parentheses are confusing me, because I’m assuming you have to keep going on the graph and use the y=mx-b formula so for the 2a-3 2b-3 and 2c-3 and you mark em as A B or C butwhat I don’t get is why is there a letter inside the parenthesis with a comma. That’s basically the only thing I don’t get.

 

[Otis]

I’m assuming you have to keep going on the graph

No, we don't use the graph. We use the given points' coordinates in the slope formula. Did you see the link in post #2? Scroll down to 'Step 1' on that page, to see an example of substituting (x,y) coordinates into the slope formula

I don’t get is why is there a letter inside the parenthesis with a comma.

Those expressions are the given coordinates for points A,B,C. For point A:

x-coordinate is the number 'a'

y-coordinate is the number '2a-3'

Have you used the slope formula before?

Can you see the slope in the given equation?

?

 

[Otis]

2x=2/1 which is the slope

Oops, I'd missed that.

2x does not equal 2/1, but the slope is 2.

It seems like you haven't learned about using the slope formula. You need to do that before working this exercise.

Do you have a textbook?

If not, then google keywords slope formula examples. There are lots of lessons on slope.

?

 

[Otis]

Did you have a chance to explore the formula? The slope between two points is the ratio comparing the difference between the points' y-coordinates to the difference between the points' x-coordinates, right?

Two other points on your line have (x,y) coordinates:

(d, 2d-3) and (e, 2e-3)

If we substitute those coordinates into the slope formula, then we get the difference between the y-coordinates (on top) and the difference between the x-coordinates (on bottom).

The difference between the y-coordinates is:

(2d - 3) - (2e - 3)

The difference between the x-coordinates is:

d - e

Therefore, the slope formula setup gives:

[imath]m = \dfrac{2d - 3 - (2e - 3)}{d - e}[/imath]

That simplifies to m = 2

Do the same with slopes AB, BC and AC. That will show Fita's claim is true.

Please share some of your work, if you'd like more guidance.

?

 

[Steven G]

I advise you to use the method by Otis in post 6 (the previous post).

An alternate proof is by using exactly what mmm4444bot said in his post. The slope between any two (different) points on a line will have the same slope. That is all you have to say!

Do you understand that the point (a, 2a-3) is on the line y =2x-3???