Question

write an equation for the line passing through B(0,3) and C(-3,4)

Answer 1

Can you calculate the slope between those two points?

Answer 2

not really?

Answer 3

@Preetha

Answer 4

Seriously? Why are you tasked with writing the equation of a line but no one ever showed you how to calculate a slope?

Have you heard or seen any of these expressions?

rise over run
change in y over change in x
vertical displacement divided by horizontal displacement
\(\dfrac{\Delta y}{\Delta x}\)

Answer 5

oh yes

Answer 6

Super. Which one is most familiar?

Answer 7

rise over run

Answer 8

Awesome. We need only two things to sort through this if we have 'rise over run".

First: B(0,3) and C(-3,4)

This notation means: B(0,3) The point B is 0 units horizontally for the Origin and 3 units vertically above the origin. C(-3,4) The point C is 3 units horizontally left of the Origin and 4 units vertically above the Origin.

Can you draw a set of coordinate axes and plot these two points?

Answer 9

yea i know how to plot them

Answer 10

Well, good. So, if you plot them, and draw the line segment between them, you can see how the line segment goes down from left to right? Starting at C and falling down to B?

Answer 11

yes

Answer 12

Perfect. This slope thing, and this is the second thing we need to know, is just a measure of how steep the fall is! (or how tough the climb if it goes up!)

We accept generally that the horizontal direction is the x-direction or x-axis and the vertical direction is the y-direction or y-axis. This means the notation B(0,3) means x = 0 and y = 3. For C, we have x = -3 and y = 4.

Do you believe?

Answer 13

yea i see that also

Answer 14

Okay, we're almost done.

RISE = How much do the y-value change? (the vertical change)
RUN = How much do the x-value change? (the horizontal change)

For B(0,3) and C(-3.4)

RISE = 4-3 = 1
RUN = -3 - 0 = -3

The ONLY really important thing is to use C first or B first in BOTH of these calculations. I used C first in both. This is very important. No switching horses in the middle of the stream.

Okay, we're just about done. Do you see where to go from here?

Answer 15

okay i got that so then would it be 1y-3x?

Answer 16

No, no.. We are just calculating the slope. The slope is RISE/RUN = 1/(-3) = -1/3. Whew!!

Okay, now that we have that, it seems prudent to remind you of the "slope-intercept" form of a line.

Have you seen y = mx+b

Answer 17

yes

Answer 18

What is 'm'?
What is "b"?

Answer 19

m=1 and b=-3? or is m the slope

Answer 20

and b is the y intercept?

Answer 21

Jumping ahead!! Let's just define. We can substitute later.

m = The Slope = RISE/RUN = -1/3
b = y-intercept

How do you suppose we should find the y-intercept?

Answer 22

um substitute 1 and -3 in ?

Answer 23

I do not know why you keep talking about 1 and -3 separately. These were intermediate values used ONLY to calculate the slope. Now that we know the slope is -1/3, we have no more relationship with 1 or -3. The slope is -1/3. That's all we know.

It can require a little more effort to find the y-intercept, but in this case, take a close look at point B(0,3). If you look hard enough, you should eventually see that this IS the y-intercept.

y = (-1/3)x + 3 -- Done!

Answer 24

oh ok

Answer 25

thank you