Question

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All help would be much appreciated! :)

Answer 1

Here is one way we can determine.
If the lines have the `same slope` they will `never` intersect.
If they have `different slopes` they will intersect at some point.


Do you remember how to find the slope of a line?\[\Large m\quad=\quad \frac{y_2-y_1}{x_2-x_1}\]

Answer 2

It's been awhile. But lemme try it out. :)

Answer 3

Hmmm I'm not sure where those squares are coming from :o

Answer 4

\[\Large \text{Maple:}\;(7,13)\;(1,5)\]For the slope of Maple street.\[\Large m_{Maple}\quad=\quad \frac{5-13}{1-7}\]

Answer 5

Oh you were working on Xylo, my bad :D

Answer 6

Ahh it's all good. So I'm supposed to multiply those numbers by two and then subtract?

Answer 7

Multiply by 2..? :o

Answer 8

\(\bf slope = m= \cfrac{rise}{run} \implies \cfrac{y_2-y_1}{x_2-x_1}\)

Answer 9

Myb bad..haha not multiply but square.

Answer 10

\(\bf slope = m= \cfrac{rise}{run} \implies \huge \cfrac{y_2-y_1}{x_2-x_1}\)

Answer 11

\[\Large \text{Maple:}\;(7,13)\;(1,5)\quad=\quad(x_1,y_1)\;(x_2,y_2)\]We plug these values into our slope formula:\[\Large m\quad=\quad \frac{y_2-y_1}{x_2-x_1}\]After we plug everything in for Maple street, and do the subtraction, we get:\[\Large m_{Maple}\quad=\quad \frac{8}{6}\]Hmmm I'm not sure where your squares are coming from :c

Answer 12

What are the numbers by x and y?

Answer 13

\(\large \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
&(7\quad ,&13)\quad &(1\quad ,&5)
\end{array}\)

Answer 14

The numbers are `subscripts`, so we can count our x's and y's.
They are not exponents.

Answer 15

Ohh okay. Well I feel quite dumb.

Answer 16

aw :c

Answer 17

@zepdrix

Answer 18

Grr sorry the site is running so slow >:c I couldn't get back here.

Answer 19

It's alright. :)

Answer 20

Next we would find the slope of Xylo Street.\[\Large (\color{#CC0033}{x_1},\;\color{#F35633}{y_1})\;(\color{#3366CF}{x_2},\;\color{#3399AA}{y_2})\quad\to\quad (\color{#CC0033}{3},\;\color{#F35633}{24})\;(\color{#3366CF}{9},\;\color{#3399AA}{32})\]Plugging these into our slope formula:\[\Large m\quad=\quad \frac{\color{#3399AA}{y_2}-\color{#F35633}{y_1}}{\color{#3366CF}{x_2}-\color{#CC0033}{x_1}}\quad=\quad \frac{\color{#3399AA}{32}-\color{#F35633}{24}}{\color{#3366CF}{9}-\color{#CC0033}{3}}\]

Answer 21

I was hoping the colors would help..
But I think it's too much color, maybe it's making it more confusing :) lol.

Answer 22

Simplify that fraction, what do you get for the slope of Xylo street? :o

Answer 23

Sorry I was away for a bit. Lemme work it out. :)

Answer 24

So the slope of Xylo street is 8/6 or 4/3.
What was the slope value we got for Maple?

Answer 25

Ooo interesting! :O The streets have the same slope.
They run `parallel` to one another.
Will they intersect?

Answer 26

Ahh I was right. Thank you! You helped me understand it a lot better. It seems pretty simple now.