Mathematics, 23.07.2019 22:30 tdahna0403

Convert each equation to slope-intercept form. (1/2) 1. y + 3 = 4(x + 6) 2. 6x + 2y = 12 3. y = -2 + 1/3(x + 9) 4. 2x - 5y = -15 5. -x - 2y = 2

Answers: 1

Show answers

Answers

Hey there, Mandoguy!

To convert each equation to slope-intercept form, first we need to distribute everything that's on the parenthesis (if it has one)
So, number one would be

1) y + 3 = 4x + 24 (I multiplied 4 times x and 4 times 6)
Now, we need to isolate y and since they are adding 3 to it, we need to subtract 3 to cancel it out. Remember what we do on one side we have to do it in the other side.
So, it would be y + 3 - 3 = 4x + 24 - 3
Number 1 would be
y = 4x + 21
y=4x+21

2) 6x + 2y = 12
Goes to
2y = 12 - 6x (I subtracted 6x from both sides to leave 2y alone)
y = 6 - 3x (I divided both sides by 2 since y it's being multiplied by 2)
y = -3x + 6 (Now, I just rearranged to make it y = mx + b
y=-3x+6

3) y = -2 + 1/3 (x + 9) In this case y is already isolated but we have parenthesis and we can't have that.
So, we distribute the number that's in front of the parenthesis to the numbers inside.
y = -2 + 1/3x + 3 (I multiplied 1/3 times x and 1/3 times 9 which is 3)
y = 1/3x + 1 (I combined like terms and rearranged to make it y=mx+b)
$y= \frac{1}{3} x+1$

4) 2x - 5y = -15 (Same as always. Isolate y. Subtract 2x from both sides)
-5y = -15 - 2x (Did you see that? We have a negative value on y and we can't have that. To fix it, we multiply both sides by -1 or just change the sign of every term)
Once you do that you will get
5y = 15 + 2x
y = 3 + 2/5 x (I divided both sides by 5 to isolate y)
y = 2/5x + 3 (Rearranged it to y = mx + b)
$y = \frac{2}{5}x + 3$

5) -x - 2y = 2 (Since the x it's being subtracted, we added to both sides)
-2y = 2 + x (See again? We have a negative value on y, so we multiply by -1 on both sides or change every sign to the opposite of itself)
So we get
2y = -2 - x (Now, we divide both sides by 2 to isolate y)
y = -1/2x - 1 (Rearranged to y = mx + b)
$y = - \frac{1}{2} x - 1$

Thanks for using !
See you soon.

Answer from: Quest

for this case we have by definition, if two lines are perpendicular, then the product of their slopes is -1.

$m_ {1} * m_ {2} = - 1$

then, given the following line:

$6x-3y = 18\\6x-18 = 3y$

$\frac {6x} {3} - \frac {18} {3} = y\\y = \frac {6x} {3} - \frac {18} {3}\\y = 2x-6$

so, $m_ {1} = 2$

we are looking for m_ {2}:

$m_{2}=\frac{-1}{m_{1}}\\m_{2}=\frac{-1}{2}\\m_{2}=-\frac{1}{2}$

then, the line is given by:

$y = - \frac {1} {2} x + b$

we find "b" replacing the given point:

$8 = - \frac {1} {2} (0) + b\\8 = b$

finally, the equation is:

$y = - \frac {1} {2} x + 8$

option c

Answer from: Quest

.95

step-by-step explanation:

Another question on Mathematics

Mathematics, 21.06.2019 15:00

Explain why the function is discontinuous at the given number a. (select all that apply.) f(x) = 1 x + 1 a = −1 f(−1) is undefined. lim x→−1+ f(x) and lim x→−1− f(x) exist, but are not equal. lim x→−1 f(x) does not exist. f(−1) and lim x→−1 f(x) exist, but are not equal. none of the above

Answers: 3

Answer

Mathematics, 21.06.2019 18:00

Lydia collected two sets of data one set of data shows an outlier. which set has an outlier, and which number is the outlier?

Answers: 2

Answer

Mathematics, 21.06.2019 21:00

Asequence has its first term equal to 4, and each term of the sequence is obtained by adding 2 to the previous term. if f(n) represents the nth term of the sequence, which of the following recursive functions best defines this sequence? (1 point) f(1) = 2 and f(n) = f(n − 1) + 4; n > 1 f(1) = 4 and f(n) = f(n − 1) + 2n; n > 1 f(1) = 2 and f(n) = f(n − 1) + 4n; n > 1 f(1) = 4 and f(n) = f(n − 1) + 2; n > 1 i will award !

Answers: 1

Answer

Mathematics, 22.06.2019 00:10

How do i take any fraction and make it into a decimal or percentage?

Answers: 1

Answer

You know the right answer?

Convert each equation to slope-intercept form. (1/2) 1. y + 3 = 4(x + 6) 2. 6x + 2y = 12 3. y = -2...

Questions

Mathematics, 07.07.2019 03:30

Describe the transformation of the parent function f(x)=x^2 to 1/2 (x+1)^2-5...