Find the equation of the line through the points (-3,-3) and (2,-1) using point-slope form. Then rewrite theequation in slope-intercept form.

Answers

Answer 1

Answer:

Answer: See below

Step-by-step explanation:

The point-slope equation is y-y₁=m(x-x₁). Since we don't know our slope, we can use the formula $m=(y_(2)-y_(1) )/(x_(2)-x_(1) )$ to find the slope. All we have to do is use the coordinate we were given and plug it into the formula.

$m=(-1-(-3))/(2-(-3)) =(2)/(5)$

Now that we have the slope, we can fill out the point-slope equation.

y-(-3)=2/5(x-(-3))

y+6=2/5(x+3)

This is the point-slope form.

Now, we can distribute and solve to get slope-intercept form.

y+6=2/5x+6/5

y=2/5x-24/5

Answer 2

Answer:

Final answer:

The equation of the line through the points (-3,-3) and (2,-1) can be found using point-slope form. It is y = (2/5)x - 9/5 in slope-intercept form.

Explanation:

To find the equation of a line using the point-slope form, we need to determine the slope of the line and use one of the given points to write the equation. Firstly, let's find the slope of the line using the formula: m = (y2 - y1) / (x2 - x1). Plugging in the coordinates (-3, -3) and (2, -1) into the formula gives us m = (-1 - (-3)) / (2 - (-3)) = 2/5. Now, we can choose one of the points (for example, (-3, -3)) and use the point-slope form equation: y - y1 = m(x - x1). Substituting the values, we get y - (-3) = (2/5)(x - (-3)). Simplifying the equation yields y + 3 = (2/5)(x + 3), which is the equation of the line in point-slope form.

To rewrite the equation in slope-intercept form y = mx + b, we need to isolate the y variable. Distributing the (2/5) to (x + 3) in the point-slope form equation gives us y + 3 = (2/5)x + 6/5. Subtracting 3 from both sides gives us y = (2/5)x + 6/5 - 3. Simplifying further, the equation becomes y = (2/5)x - 9/5. Therefore, the equation of the line through (-3, -3) and (2, -1) in slope-intercept form is y = (2/5)x - 9/5.

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How do you find an equation of the sphere with center (4,3,5) and radius √6?

Answers

Answer:

$(x-4)^2+(y-3)^2+(x-5)^2=6$

Step-by-step explanation:

The the center of the sphere is given as (a,b,c) and the radius is r, then the equation of the sphere would be:

$(x-a)^2+(y-b)^2+(x-c)^2=r^2$

From the info, we can say:

a = 4

b = 3

c = 5

r = $√(6)$

Plugging into formula we get the equation:

$(x-a)^2+(y-b)^2+(x-c)^2=r^2\n(x-4)^2+(y-3)^2+(x-5)^2=(√(6) )^(2) \n(x-4)^2+(y-3)^2+(x-5)^2=6$

Remember to use

. Emma is making bracelets for her friends. She noticed that 12 out of 20 of her beads are red. What decimal is equivalent to the fraction of Emma's beads that are red?

Answers

Answer:

0.6

Step-by-step explanation:

12/20 = 6/10 = 0.6

The product of two numbers is 16/3 if one of the number is 48/5 what is the other one?

Answers

Answer:

The other number is 5/9.

Step-by-step explanation:

16/3 = 48/5 * x

x = 5/9

If the principal is $350 and the interest rate is 3 percent, what is the simple interest earned in one year?simple interest = Pxrxt

Answers

Answer:

The simple interest was found to be $9.6 after 1 year at 3%

Step-by-step explanation:

Given that

principal p= $350

rate r= 3%= 3/100= 0.03

time t= 1 year

The expression for the simple interest is given as

SI= p*r*t

SI= 320*0.03*1

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After 1 year at 3% the simple interest is $9.6

Simply put the extra money earned after an investment is called the simple interest

Jake buys a gaming system and equipment for $2200.00 with a credit card that has a 28% APR. He makes a $100.00 monthly payment. What is the total amount of interest based on the APR? Enter your answer as a dollar amountsuch as: $324.

Answers

Answer:

Rounding to the next dollar, the total amount of interest paid by Jake is $ 923.00

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Gaming system and equipment cost = $ 2,200

Annual interest rate = 28%

Monthly payment = $ 100

2. What is the total amount of interest based on the APR?

Using Excel, we calculated the total number of months to pay the gaming system and the total interest, as you can read below.

Rounding to the next dollar, the total amount of interest paid by Jake is $ 923.00

Answer: $922

Step-by-step explanation:

I just did it and got it right. make sure to put $ or you will get it wrong

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Answers

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