Can anyone help???

- isuckatschool43

Can anyone help???

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- isuckatschool43

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- isuckatschool43

@sleepyjess

- isuckatschool43

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## More answers

- johnweldon1993

We simply need to find the equations of both lines, since we are given 2 points in each case that is all we need
Remember the equation of a line \(\large y = mx + b\)
where the slope \(\large m = \frac{y_2 - y_1}{x_2 - x_1}\) and b *the y-intercept* can be found by using one of the points
So, can you calculate the slope for the first line?

- mathmale

If you do this correctly, y ou'll end up with a system of linear equations in two variables.
Which methods of solving such systems do you know? apply one of them to find your solution.

- isuckatschool43

@johnweldon1993 the slope for the first line is 4/3

- johnweldon1993

Not quite, can you show me what you did?

- isuckatschool43

i dont really know. ive been working on this problem for 5 hours

- johnweldon1993

Well dont stress out about it, math is easy once you can see why it works
So the first line...goes through 2 points \(\large (-1,7)\) and \(\large (5,13)\)
Let (-1,7) = (x1,y1) and (5,13) = (x2,y2)
So for the slope equation we have
\[\large m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{13 - 7}{5 - (-1)} = \frac{6}{6} = 1\]
Right?

- isuckatschool43

right

- johnweldon1993

Let continue on with this line for now
Pick one of the 2 points..either one which do you want to work with?

- isuckatschool43

(5,13)

- johnweldon1993

Alright, so remember the slope of a line \(\large y = mx + b\)
We just found 'm' to be 1...so we have
\[\large y = 1x + b\]
Now lets work with the point you chose, (5,13) ...remember that looks like (x,y) so if we plug those coordinates in...we go from \(\large y = 1x + b\) to \(\large 13 = 5 + b\)
If we solve for 'b' what would we get?

- isuckatschool43

11?

- johnweldon1993

Not quite
the equation we have is
\[\large 13 = 5 + b\]
how would we solve for 'b' ?? 5 plus what number = 13?

- isuckatschool43

8

- johnweldon1993

There ya go...so we found that 'm' = 1 and we just found 'b' = 8
So the equation for the first line is \(\large y = x + 8\)
make sense so far?

- isuckatschool43

yes

- johnweldon1993

Great! So now the second line...tell me what the slope would be?

- isuckatschool43

-3

- johnweldon1993

perfect! Can you solve for 'b' now as well?

- isuckatschool43

11

- johnweldon1993

Awesome!
So that makes the second line \(\large y = -3x + 11\)

- johnweldon1993

So now, we have 2 lines
\(\large y = x + 8\) and \(\large y = -3x + 11\)
We need to find where these 2 cross, how would we do that?

- isuckatschool43

x+8 = -3x+11?

- johnweldon1993

Exactly! the y-coordinate would be the same so we can set the 2 equations equal to each other
So solving that for 'x' what do you get?

- isuckatschool43

3/4

- johnweldon1993

There ya go, I'll trust you can plug that into either equation and solve for 'y' as well, however there IS only 1 choice with x = 3/4

- isuckatschool43

b

- johnweldon1993

And you're all set!

- isuckatschool43

thx

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