Mathematics, 25.08.2019 00:00 mistydsargentp5wrh4

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

Answers: 1

Show answers

Answers

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

i think it might be a but you might want a second opinion

Alexa and bart are arguing about who will do the dishes. how can they make a fair decision selection

Answer from: Quest

Hello!

the answer is:

$\frac{3^{4} }{3^{1}}=3^{3}$

why?

to solve the problem, we need to remember the quotient of power property, it's defined by the following relation:

$\frac{a^{m} }{a^{n} }=a^{m-n}$

if we have a quotienf of powers that have the same base, we need to keep the same base and subtract the exponent of the denominator power to the exponent of the numerator power.

so, we are given the expression:

$\frac{3^{4} }{3^{1}}$

then, calculating we have:

$\frac{3^{4} }{3^{1}}=3^{4-1}=3^{3}$

hence, the answer is:

$\frac{3^{4} }{3^{1}}=3^{3}$

have a nice day!

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 23:00, utjfkdndidndldn62121

Why is it so easy to buy on impulse and overspend with a credit card? what could you do to counteract this tendency?

Answers: 1

continue

Mathematics, 22.06.2019 00:00, makikorising1226

Afair survey question is one that does not encourage biased responses. which survey question is fair? a.) do you agree that only unethical people take credit for other people’s work? b.) have you ever taken credit for somebody else’s work? c.) have you ever engaged in unethical behavior, such as taking credit for somebody else’s work? d.) don’t you think it is unethical to take credit for somebody else’s work?

Answers: 1

continue

Mathematics, 22.06.2019 00:00, Geo777

How many quarts of a 50% solution of acid must be added to 20 quarts of a 20% solution of acid in order to get a 40% solution of acid?

Answers: 2

continue

Mathematics, 22.06.2019 03:00, Peggy1621

Afitness center has 2 membership plans one has a low dollar sign up fee of 15 dollars and costs 38 dollars per month to join. a second plan has a higher sign up fee of 78 dollars but a lower monthly fee of 31 dollars for what number of days of the month is the coat the same