Y=mx+b
x=number of newspapers
37.5 earned for 5 newspapers
37.5=5m+b

earned 75 and deliverd 20 newpapers
75=20m+b

we have

37.5=5m+b and
75=20m+b
multiply first equaiton by -1 and add to other equaiton

-37.5=-5m-b
<u>75=20m+b +</u>
37.5=15m+0b

37.5=15m
divide both sides by 15
2.5=m

sub back to find b
75=2.5(20)+b
75=50+b
minsu 50 both sides
25=b

y=2.5x+25 is lnear funtion

7 0

3 years ago

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Use the Distance Formula and the Pythagorean Theorem to find the distance between each pair of points. M (10, −4) and N (2, −7)

xenn [34]

Answer:

$d=\sqrt{73}\approx8.54$

Step-by-step explanation:

So we have the two points (10,-4) and (2,-7).

And we want to find the distance between them using the Distance Formula and the Pythagorean Theorem. Let's do each one individually.

1) Distance Formula.

The distance formula is:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2$

Let's let (10,-4) be (x₁, y₁) and let's let (2,-7) be (x₂, y₂). So:

$d=\sqrt{((2)-(10))+((-7)-(-4))^2$

Simplify:

$d=\sqrt{(2-10)^2+(-7+4)^2$

Subtract:

$d=\sqrt{(-8)^2+(-3)^2$

Square:

$d=\sqrt{64+9}$

Add:

$d=\sqrt{73}$

Approximate:

$d\approx8.54$

So, the distance between (10,-4) and (2,-7) is approximately 8.54 units.

2) Pythagorean Theorem

Please refer to the graph.

So, we want to find the distance. This will be the length of the red line, or the hypotenuse.

First, let's find the length of the two legs.

The longer leg will be the difference between the two x-coordinates. So, the length of the longer leg is:

$(10-2)=8$

Note: It doesn't matter if we do 2-10, which gives -8, since we are going to square anyways. Also, distance is always positive, so 8 would be our answer.

And the shorter leg is the difference between the two y-coordinates. Namely:

$(-7-(-4))=-3=3$