Answer in simplest form

Find the equation of the line that contains the given point and the given slope. Write the equation in slope-intercept form.

stealth61 [152]

The slope-point form of a line:

$y-y_0=m(x-x_0)$

The slope-intercept form of a line:

$y=mx+b$

1.

$m=6,\ (4,\ 1)\to x_0=4,\ y_0=1$

Substitute

$y-1=6(x-4)\qquad|\text{use distributive property}\\\\y-1=6x-24\qquad|\text{add 1 to both sides}\\\\\boxed{y=6x-23}$

2.

$m=-5,\ (6,\ -3)$

Substitute

$y-(-3)=-5(x-6)\qquad|\text{use distributive property}\\\\y+3=-5x+30\qquad|\text{subtract 5 from both sides}\\\\\boxed{y=-5x+24}$

3.

$m=-\dfrac{1}{2},\ (-8,\ 2)\\\\y-2=-\dfrac{1}{2}(x-(-8))\\\\y-2=-\dfrac{1}{2}(x+8)\\\\y-2=-\dfrac{1}{2}x-4\qquad|\text{add 2 to both sides}\\\\\boxed{y=-\dfrac{1}{2}x-2}$

4.

$m=0,\ (-7,\ -1)\\\\y-(-1)=0(x-(-7))\\\\y+1=0\qquad|\text{subtract 1 from both sides}\\\\\boxed{y=-1}$

3 0

3 years ago

A factory produces 80,000 candies each day they produce equal quantities of for flavor cherry ,Lemon , orange , and strawberry.T

Serhud [2]

Answer:

The probably of randomly selecting an orange flavoured candy is 1/4 or 0.25

Step-by-step explanation:

Extracting the key information from the question asked:-

*** A factory produces 80,000 candies

*** Everyday of the week, they produce equal quantities of candies with varieties of flavours like cherry, lemon, orange and strawberry.

*** The candies are mixed up while packaging.

*** We are simply required to find or calculate the probability that one randomly selected candy from the pack is orange flavoured candy.

From the question, we were informed that a particular company has the capacity of producing 80,000 candies everyday. The company also produces these candies in four separate flavours. This now means that the number of orange candies produced will be the same as the number of strawberry candies produced and this will also be equal to the number of cherry candies produced and then the same as the number of lemon flavours made.

That is:

Number of lemons = number of strawberries = number of cherries = number of orange flavours.

80,000 candies are produced everyday. In order to calculate the number of equal proportions of strawberry/cherry/orange/lemon candies made per day, we will simply have to divide the total number of candies produced per day by the number of flavours available:

= 80,000/4

= 20,000

Therefore, 20,000 candies of each of the four different flavours are produced by the company per day.

Now, the probability of randomly selecting an orange candy is

= the number of orange candies made per day/total number of candies produced per day

P(orange candy)

= 20,000/80,000

= 1/4

= 0.25

The probability of randomly selecting an

orange candy is 1/4 or 0.25

4 0

4 years ago

How do you solve 5y+34=-2 (1-7y)

sergiy2304 [10]

You just kind of do it

6 0

3 years ago

Read 2 more answers

a box with a square base and open top must have a volume of 70304 c m 3 cm3 . we wish to find the dimensions of the box that min

Dmitriy789 [7]

The box should have base 52 cm by 52 cm and height 26 cm.

What is volume?

A three-dimensional space's occupied volume is measured. It is frequently expressed as a numerical value using SI-derived units, other imperial units, or US customary units. Volume definition and length definition are connected.

The Volume of a box with a square base x by x cm and height h cm is

$V = x^2h$