Question

Can anyone help???

Answer 1

@sleepyjess

Answer 2

k

Answer 3

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?

Answer 4

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.

Answer 5

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

Answer 6

Not quite, can you show me what you did?

Answer 7

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

Answer 8

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?

Answer 9

right

Answer 10

Let continue on with this line for now

Pick one of the 2 points..either one which do you want to work with?

Answer 11

(5,13)

Answer 12

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?

Answer 13

11?

Answer 14

Not quite

the equation we have is

\[\large 13 = 5 + b\]

how would we solve for 'b' ?? 5 plus what number = 13?

Answer 15

8

Answer 16

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?

Answer 17

yes

Answer 18

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

Answer 19

-3

Answer 20

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

Answer 21

11

Answer 22

Awesome!

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

Answer 23

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?

Answer 24

x+8 = -3x+11?

Answer 25

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?

Answer 26

3/4

Answer 27

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

Answer 28

b

Answer 29

And you're all set!

Answer 30

thx