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sleet_krkn [62]
3 years ago
6

When you use the distance formula, does the order in which you subtract the x- and y- coordinates matter? Explain please

Mathematics
1 answer:
vladimir1956 [14]3 years ago
6 0
Lets say ur points are (1,2)(3,4)

d = sqrt (x2 - x1)^2 + (y2 - y1)^2

u would label ur points
set 1 (1,2)...x1 = 1 and y1 = 2
set 2 (3,4)...x2 = 3 and y2 = 4

or u could label them this way..
set 1 (3,4)...x1 = 3 and y1 = 4
set 2 (1,2)...x2 = 1 and y2 = 2

u have to do (x2 - x1)^2 and (y2- y1)^2....but u can label ur sets of points different. Just make sure u keep ur sets together. Does that make sense ?
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The line through (-1/2, -7/2) and (2, 14) in slope intercept form??
icang [17]
To find the equation of a line in slope-intercept form given two points, we must arrange the points this way to find the slope (m):

m =  \frac{y_{2}-y _{1}}{x_{2}-x_{1}}

We can replace the variables in this equation with the values from the points we have been given, (\frac{-1}{2},  \frac{-7}{2}) and (2, 14). We know that the x-values always come first in an ordered pair, so we can put those in our equation first.
It doesn't really matter which x-value goes in which x-value slot in the equation as long as you match up the y-values in the same fashion. But for the sake of convenience, we will call the 2 in the second ordered pair x_{2} and the \frac{-1}{2} in the first ordered pair x_{1}.
Now, we can match these values in our equation, and while we're at it, we can substitute the appropriate y-values into their places as well.

m =  \frac{y_{2}-y _{1}}{x_{2}-x_{1}}

m =  \frac{14 -  \frac{-7}{2} }{2 -  \frac{-1}{2} }

Now, we can see that we are subtracting negatives in this equation. Remember that whenever you subtract a negative, it is the same as adding a positive. So, this equation could be rewritten as

m =  \frac{14 +  \frac{7}{2} }{2 +  \frac{1}{2} }

and we can change the improper fraction in the numerator into a mixed number for ease of addition.

m =  \frac{14 + 3 \frac{1}{2} }{2+ \frac{1}{2} }

And here, we can add, since it's made simple for us.

m =  \frac{17  \frac{1}{2} }{2  \frac{1}{2} }

Finally, to get the slope we can complete the fraction by dividing.

17.5 ÷ 2.5 = 7

The slope of this equation, m, is 7, and so far, our equation looks like this:

y = 7m + b

Now, to find y-intercept.

To do this, we simply have to substitute one of the ordered pairs in for the appropriate x- and y-values and solve. To make it easier on ourselves, we can use (2, 14) so we don't have to deal with negative numbers or fractions.

y = 7x + b

Let us substitute in our values.

14=7(2)+b

Now, we can solve by multiplying the 7 and 2.

14=14+b

Here, we can subtract 14 from both sides, since it is added to both in the equation, and we are left with

0 = b

which can be flipped around to show

b=0

The y-intercept of this line is 0.

Now, we can make this known in our equation like this:

y=7x+0

Or, for neatness' sake, we can just say

y=7x

which is your final equation.

The line through (\frac{-1}{2},  \frac{-7}{2}) and (2, 14) in slope-intercept form is <span>y=7x.
Hope that helped! =) </span>


7 0
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