Help me graph the line through the point P having slope m. Find the coordinates of two other points on the line.
34. P(-3,-1), m=0.75

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@Loser66 @SolomonZelman @zepdrix @Hero @Jaynator495

- zepdrix

Since we're given a `slope` and a `point`,
it's probably best to write the equation for our line in `point slope form`.

- zepdrix

So here is what point-slope looks like:\[\large\rm y-\color{orangered}{y_o}=m(x-\color{orangered}{x_o})\]Where \(\large\rm (\color{orangered}{x_o},~\color{orangered}{y_o})\) is the given point.

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- zepdrix

Plugging in our values gives us,\[\large\rm y-\color{orangered}{(-3)}=0.75(x-\color{orangered}{(-1)})\]Simplifies to,\[\large\rm y+3=0.75(x+1)\]

- zepdrix

This will help us find other points on the line.

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nice! Thanks for the clarification!

- zepdrix

To graph it easily, we just need one more point.
Then we can draw a line through the two points.

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Yup I figured. I just got confused when it asked me to find another sets of points

- zepdrix

Ahh woops! I plugged the numbers in backwards!! :O
Notice I plugged the -3 into the y.

- zepdrix

\[\large\rm y+1=0.75(x+3)\]My bad >.<
Our point was this: \(\large\rm P(-3,-1)\)
It was NOT this \(\large\rm (-1,-3)\) which is what I plugged in at the start.

- zepdrix

So we need another point? Hmm...
Let's plug in x=0 and see if we can come up with something.

- zepdrix

\[\large\rm y+1=0.75(0+3)\]So we're currently working on finding this point: \(\large\rm (0,?)\)
We're choosing 0 for x,
and we're going to solve this equation for y to see the corresponding coordinate value.

- zepdrix

Understand how to solve for y in that setup? :o

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Yuup! Also could you help me out with a word problem related to slope?

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A ramp to provide handicapped people access to a certain building is to be constructed with a slope of 5%. If the entrance to the building is 3 ft above ground level, how long should the base of the ramp be?

- zepdrix

\(\large\rm m=5\text{%}\)
So it would be nice if we could write this as an actual number, not a percentage.
Do you remember how to convert it? :)

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hmm is it out of 100? I have no clue

- zepdrix

Yes, `per` `cent` means `per` `100`.
Think of the word `century`, which measures 100 years.
So 5% means, 5 per 100.
So we can write that as a fraction: \(\dfrac{5}{100}\)

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so thats the slope?

- zepdrix

\[\large\rm m=\frac{5}{100}\]Yes, that's the slope.
Let's simplify it down.
Both top and bottom are divisible by 5.

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so 1/20

- zepdrix

|dw:1443660767334:dw|

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wOw nice drawing!

- zepdrix

|dw:1443660878426:dw|

- zepdrix

Do you remember your slope formula?
Finding the slope of a line, given two points?

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y2-y1/x2-x1 so x-0/3-0 =x/3?

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ops nvm m=3/x

- zepdrix

Mmm ok good!
\[\large\rm m=\frac{y_2-y_1}{x_2-x_1}=\frac{3-0}{x-0}\]But recall that we actually KNOW the value of m, let's plug it in!\[\large\rm \frac{1}{20}=\frac{3}{x}\]And solve for x.

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x=60!

- zepdrix

yay good job \c:/
now the guy in the chair can safely get up the ramp

- zepdrix

or down

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Thanks for the major help! There needs to be more people like you

- zepdrix

:3

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