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2 years ago

What is (-4, 6) and (0, 7) in slope intercept form? :) thank you

Mathematics

1 answer:

gavmur [86]2 years ago

6 0

Answer:

y = 1/4x + 7

Step-by-step explanation:

(-4, 6) and (0, 7)

First you want to find the slope of the line that passes through these points. To find the slope of the line, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)

Plug in these values:

(7 - 6) / (0 - (-4))

Simplify the parentheses.

= (1) / (0 + 4)

= (1) / (4)

Simplify the fraction.

= 1/4

This is your slope. Plug this value into the standard slope-intercept equation of y = mx + b.

y = 1/4x + b

To find b, we want to plug in a value that we know is on this line: in this case, I will use the second point (0, 7). Plug in the x and y values into the x and y of the standard equation.

7 = 1/4(0) + b

To find b, multiply the slope and the input of x(0)

7 = 0 + b

Now, isolate b.

7 = b

Plug this into your standard equation.

y = 1/4x + 7

This is your equation.

Check this by plugging in the other point you have not checked yet (-4, 6).

y = 1/4x + 7

6 = 1/4(-4) + 7

6 = -1 + 7

6 = 6

Your equation is correct.

Hope this helps!

You might be interested in

A cylinder shaped can needs to be constructed to hold 500 cubic centimeters of soup. The material for the sides of the can costs

iogann1982 [59]

Answer:

r=3.628cm

h=12.093cm

Step-by-step explanation:

For this problem we are going to use principles, concepts and calculations from multivariable calculus; mainly we are going to use the Lagrange multipliers method. This method is thought to help us to find a extreme value of a multivariable function 'F' given a restriction 'G'. F represents the function that we want to optimize and G is just a relation between the variables of which F depends. The Lagrange method for just one restriction is:

$\nabla F=\lambda \nabla G$

First, let's build the function that we want to optimize, that is the cost. The cost is a function that must sum the cost of the sides material and the cost of the top and bottom material. The cost of the sides material is the unitary cost (0.03) multiplied by the sides area, which is $A_s=2\pi rh$ for a cylinder; while the cost of the top and bottom material is the unitary cost (0.05) multiplied by the area of this faces, which is $A_{TyB}=2\pi r^2$ for a cylinder.

So, the cost function 'C' is:

$C=2\pi rh*0.03+2\pi r^2*0.05\\C=0.06\pi rh+0.1\pi r^2$

The restriction is the volume, which has to be of 500 cubic centimeters:

$V=500=\pi r^2h\\500=\pi hr^2$

So, let's apply the Lagrange multiplier method:

$\nabla C=\lambda \nabla V\\\frac{\partial C}{\partial r}=0.06\pi h+0.2\pi r\\\frac{\partial C}{\partial h}=0.06\pi r\\\frac{\partial V}{\partial r}=2\pi rh\\\frac{\partial V}{\partial h}=\pi r^2\\(0.06\pi h+0.2\pi r,0.06\pi r)=\lambda (2\pi rh,\pi r^2)$

At this point we have a three variable (h,r, λ)-three equation system, which solution will be the optimum point for the cost (the minimum). Let's write the system:

$0.06\pi h+0.2\pi r=2\lambda \pi rh\\0.06\pi r=\lambda \pi r^2\\500=\pi hr^2$

(In this kind of problems always the additional equation is the restricion, in this case, V=500).

Let's divide the first and second equations by π:

$0.06h+0.2r=2\lambda rh\\0.06r=\lambda r^2\\500=\pi hr^2$

Isolate λ from the second equation:

$\lambda =\frac{0.06}{r}$

Isolate h from the third equation:

$h=\frac{500}{\pi r^2}$

And then, replace λ and h in the first equation:

$0.06*\frac{500}{\pi r^2} +0.2r=2*(\frac{0.06}{r})r\frac{500}{\pi r^2} \\\frac{30}{\pi r^2}+0.2r= \frac{60}{\pi r^2}$

Multiply all the resultant equation by $\pi r^{2}$ :

$30+0.2\pi r^3=60\\0.2\pi r^3=30\\r^3=\frac{30}{0.2\pi } =\frac{150}{\pi}\\r=\sqrt[3]{\frac{150}{\pi}}\approx 3.628cm$

Then, find h by the equation $h=\frac{500}{\pi r^2}$ founded above:

$h=\frac{500}{\pi r^2}\\h=\frac{500}{\pi (3.628)^2}=12.093cm$

4 0

3 years ago

After ordering the data set, what is the next step in drawing a box plot that shows the distribution of the amounts spent? 1. Ma

vodka [1.7K]

Answer:

2. Find the five boundary values

Step-by-step explanation:

When drawing a dot, the steps are;

i) The data set (the list of numbers to be presented in the dot plot) are arranged in increasing order from left to right, with thee lowest value on the left and the highest value located at the right of the list

ii) The five boundary values are listed as follows;

The Minimum and Maximum Values

1) The minimum value is the lowest number in the list, which is the first number from the left

2) The maximum value is the final number on the right of the list

3) The Median, Q₂

The median number is the number which divides the data arranged in increasing number, into two equal parts

The First Quartile and Third Quartile

The numbers are divided from the median, such that the Lower half is to the left of the Median, and the Upper half is to the right of median

4) The First Quartile, Q₁ = The median of the Lower half

5) The Third Quartile, Q₂ = The median of the Upper half

iii) The box plot is then drawn with the five boundary values found above