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2 years ago

What is the equation of the line that passes through the point (-6,8) and has a slope of -5/3?

Mathematics

1 answer:

Alexxx [7]2 years ago

7 0

Answer:

y = -5/3 - 8

Step-by-step explanation:

We want to write this in the form y = mx + b. We need to find the m (slope) and the b (y-intercept) , Whew, they already gave us the slope, so we are have way there. I will plug in the x and y that we are given from the point (-6, 8) to solve for b.

y = mx + b

8 = -5/3(-6) + b Multiply the fraction by -6

8 = 30/3 + b I can make 6 a fraction by writing it 6/1 and then just multiply straight across. A negative times a negative is a positive.

8 = 10 + b 30/3 is equal to 10. Now subtract 10 from both sides to get b

-8 = b

I can now write the equations since I now know m and b.

y = -5/3 + (-8) which is the same as y = -5/3 - 8. Adding a negative is the same as subtracting a positive.

You might be interested in

Find Mx, My, and (x, y) for the lamina of uniform density rho bounded by the graphs of the equations. y = x2/3, y = 0, x = 1

erik [133]

Answer:

$\mathbf{(\overline x , \overline y ) = (\dfrac{5}{8}, \dfrac{5}{14})}$

Step-by-step explanation:

Given that:

$y = x^{2/3}$ at y = 0 , x = 1

Then:

Area = $\int^{1}_{0} x^{2/3} \ dx$

Area = $\begin {bmatrix} \dfrac{3}{5}x^{5/3} \end {bmatrix} ^1_0$

Area = $\dfrac{3}{5}$

Then:

$\overline x = \dfrac{1}{A} \int^b_a x (f(x) -g(x) ) \ dx$

$\overline x = \dfrac{5}{3} \int^1_0 x (x^{2/3} -0 ) \ dx$

$\overline x = \dfrac{5}{3} \int^1_0 x^{5/3} \ dx$

$\overline x = \dfrac{5}{3} \ [\dfrac{3}{8}x^{8/3}]^1_0$

$\overline x = \dfrac{5}{3} \times \dfrac{3}{8}$

$\overline x = \dfrac{5}{8}$

Similarly;

$\overline y = \dfrac{1}{A} \int^b_a \dfrac{1}{2} \begin{bmatrix} (f(x)^)2 - (g(x))^2 \end {bmatrix} \ dx$

$\overline y = \dfrac{5}{3} \int^1_0 \dfrac{1}{2} \begin{bmatrix} (f(x^{2/3})^2 -0 \end {bmatrix} \ dx$

$\overline y = \dfrac{5}{3} \int^1_0 \dfrac{1}{2} \begin{bmatrix} (x^{4/3} ) \end {bmatrix} \ dx$

$\overline y = \dfrac{5}{3} \begin{bmatrix} \dfrac{1}{2} (x^{7/3} ) \times \dfrac{3}{7} \end {bmatrix} ^1_0$

$\overline y = \dfrac{5}{3} \begin{bmatrix} \dfrac{3}{14} (x^{7/3} ) \end {bmatrix} ^1_0$

$\overline y = (\dfrac{5}{3} \times \dfrac{3}{14} )$

$\overline y = \dfrac{5}{14}$

Thus; $\mathbf{(\overline x , \overline y ) = (\dfrac{5}{8}, \dfrac{5}{14})}$

4 0

3 years ago

64 ounces in 8 cups unit rate

Veseljchak [2.6K]

So the unit rate is basically how many ounces in 1 cup?

So since there are 64 ounces in 8 cups, you can just divide by 8, to find how many sets of 8 there are in 64.

64 = 8

64 / 8 = 8 / 8

8 = 1

So there are 8 ounces in 1 cup, which is your unit rate.

7 0

3 years ago

On a coordinate plane, a rectangle has points K prime (1, 3), L prime (2, 3), M prime (2, negative 3), N prime (1, negative 3).

cupoosta [38]

Answer:

C and E

Step-by-step explanation: Did it on the edgenuity test. Good luck!

5 0

3 years ago

Read 2 more answers

Carol has some dimes and quarters. If she has 31 coins worth a total of $4.30, how many of each type of coin does she have?

sasho [114]

Answer:

23 Dimes and 8 Quarter.

Step-by-step explanation:

Important info:

31 Coins worth a total of $4.30

Note:

Dimes = .10

Quarters = .25

10 Dimes = 1.00

4 Quarter = 1.00

Question to Answer:

How many of each type of coin does she have?

Solution:

Lets get rid of the .30 cent in $4.30 so

.30 = 3 Dimes

Now $4.00,

4.00-1.00 of quarter

3.00 and 4 quarter..

Right now we have 3 Dimes and 4 Quarter = $1.30.

And that 7 Coins worth of $1.30.

3.00-2.00= 1.00 and 20 Dimes so now we have

23 Dimes and 4 Quarter.

And that add up to 27.

1.00-1.00 of Quarter = 4 Quarter.

so 31 worth a total of $4.30.

So that's 23 Dimes and 8 Quarter.

Check Work:

23 Dimes = $2.30 and 8 Quarter = $2.00

$2.30 + $2.00 = 4.30

Hence, The Correct Answer is 23 Dimes and 8 Quarter.

~[ RevyBreeze }~

5 0

3 years ago

What is the solution to 0.4(12-3x)=0.3(12x-16)

Pavel [41]

Step 1: Simplify both sides of the equation.

0.4(12−3x)=0.3(12x−16)

(0.4)(12)+(0.4)(−3x)=(0.3)(12x)+(0.3)(−16)(Distribute)

4.8+−1.2x=3.6x+−4.8

−1.2x+4.8=3.6x−4.8

Step 2: Subtract 3.6x from both sides.

−1.2x+4.8−3.6x=3.6x−4.8−3.6x

−4.8x+4.8=−4.8

Step 3: Subtract 4.8 from both sides.

−4.8x+4.8−4.8=−4.8−4.8

−4.8x=−9.6

Step 4: Divide both sides by -4.8.

−4.8x /−4.8 = −9.6 /−4.8

x = 2

6 0

3 years ago