Mathematics, 25.08.2019 00:00 mistydsargentp5wrh4

The line through (-1/2, -7/2) and (2, 14) in slope intercept form? ?

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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 (

):

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

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,

, 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 y=7x

.
Hope that helped! =)

Answer from: Quest

when functions are first introduced, you will probably have some simplistic "functions" and relations to deal with, usually being just sets of points. these won't be terribly useful or interesting functions and relations, but your text wants you to get the idea of what the domain and range of a function are. small sets of points are generally the simplest sorts of relations, so your book starts with those.

step-by-step explanation:

state the domain and range of the following relation. is the relation a function?

{(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)}

the above list of points, being a relationship between certain x's and certain y's, is a relation. the domain is all the x-values, and the range is all the y-values. to give the domain and the range, i just list the values without duplication:

domain: {2, 3, 4, 6}

range: {–3, –1, 3, 6}

(it is customary to list these values in numerical order, but it is not required. sets are called "unordered lists", so you can list the numbers in any order you feel like. just don't duplicate: technically, repetitions are okay in sets, but most instructors would count off for this.)

while the given set does indeed represent a relation (because x's and y's are being related to each other), the set they gave me contains two points with the same x-value: (2, –3) and (2, 3). since x = 2 gives me two possible destinations (that is, two possible y-values), then this relation is not a function.

note that all i had to do to check whether the relation was a function was to look for duplicate x-values. if you find any duplicate x-values, then the different y-values mean that you do not have a function. remember: for a relation to be a function, each x-value has to go to one, and only one, y-value.

state the domain and range of the following relation. is the relation a function?

{(–3, 5), (–2, 5), (–1, 5), (0, 5), (1, 5), (2, 5)}

i'll just list the x-values for the domain and the y-values for the range:

Answer from: Quest

Photo math will give you the step by step answer : )