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ryzh [129]
2 years ago
12

Graph the line that passes through the points (-4,-6) and (-2,-7) and

Mathematics
1 answer:
Komok [63]2 years ago
3 0

Answer:

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

Step-by-step explanation:

(-4,-6)(-2,-7)

Step 1. Find the slope (by using the slope-formula)

m = slope

m=\frac{y_2-y_1}{x_2-x_1}

m=\frac{-7--6}{-2--4}

m=\frac{-1}{2}

m=-\frac{1}{2}

Step 2. Create the equation of a line that has a slope of -\frac{1}{2}

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

Step 3. Find the y-intercept

To do this, use any of the two points and substitute their x and y values

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

point: (-2,-7)

(-7)=-\frac{1}{2}(-2)+b

(-7)=1+b

b=-7-1

b=-8

Step 4. Write the equation in Slope-intercept form

y=mx+b

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

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You design a tree house using a coordinate plane in which the coordinates are measured in feet. The vertices of the floor are (-
Nikitich [7]

Answer:

Perimeter = 28 yards

Area = 49 square yards.

Step-by-step explanation:

Distance formula:

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Let as consider the vertices of the floor are A(-2,-3), B(-2,4), C(5,4) and D(5,-3).

Using distance formula, we get

AB=\sqrt{(-2-(-2))^2+(4-(-3))^2}=\sqrt{(-2+2)^2+(4+3)^2}=\sqrt{0+7}^2=7

Similarly,

BC=\sqrt{(5-(-2))^2+(4-4)^2}=7

CD=\sqrt{(5-5)^2+(4-(-3))^2}=7

AD=\sqrt{(5-(-2))^2+(-3-(-3))^2}=7

It is conclude that, AB=BC=CD=AD.

From the given points it is clear that all sides lie on either vertical or horizontal lines.

Since all sides are equal, and adjacent sides are perpendicular, therefore, the base is a square with edge 7 yards.

Perimeter of square floor is

P=4a=4(7)=28\text{ yards}

Area of square floor is

A=a^2=7^2=49\text{ sq. yards}

Therefore, the perimeter is 28 yards and the area is 49 square yards.

7 0
3 years ago
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Answer:

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6 0
3 years ago
Four more than three times a number is thirteen. What is this number?
Ostrovityanka [42]

Answer:

3

Step-by-step explanation:

13-4=9

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4 0
2 years ago
Read 2 more answers
1. You are standing on top of a ridge using a clinometer trying to figure out how far your dog has wandered off in
olga_2 [115]

<u>Given:</u>

It is given that the ridge is 360 inches tall.

<u>Assumptions:</u>

Assume you are 170.1 cm tall which equals 67 inches tall, the height from your eye to the floor is 360+67 = 427 inches.

The distance from your eye level to the bottom of the ridge is 427 inches.

Assume the angle A is 60°.

<u>To find the distance from you to your dog.</u>

<u>Solution:</u>

A right-angled triangle can be formed where the angle is 60°, the distance between you and the dog is the hypotenuse of the triangle and your height from the floor is the adjacent side of the triangle.

Assume the hypotenuse of the triangle measures x inches.

To determine the length of the hypotenuse, we determine the cos of the angle.

cos \theta = \frac{adjacent side}{hypotenuse} .

cos A = \frac{427}{x} , x = \frac{427}{cos60} , cos60=0.5.

x=\frac{427}{0.5} = 854.

So if the ridge is 360 inches tall and you are 67 inches tall and the angle A is 60°, the distance between your dog and you is 854 inches.

3 0
3 years ago
What is the equation of the following line written in slope-intercept form -2/3 and -1/-4? y = -11x - 7 y = -7x + 11 y = -7x - 1
Snowcat [4.5K]

Answer:

y=-7x-11

Step-by-step explanation:

Given:

The two points on the line are (-2,3) and (-1,-4).

The slope of the line joining two points (x_{1},y_{1}) and (x_{2},y_{2}) is given as:

Slope,m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}

Here, x_{1}=-2,y_{1}=3,x_{2}=-1,y_{2}=-4

∴ m=\frac{-3-4}{-1-(-2)}=\frac{-7}{-1+2}=\frac{-7}{1}=-7

Equation of line with a point (x_{1},y_{1}) and slope m is given as:

y-y_{1}=m(x-x_{1})

Plug in -2 for x_{1}, 3 for y_{1} and -7 for m. This gives,

y-3=-7(x-(-2))\\y-3=-7(x+2)\\y-3=-7x-(7\times 2)\\y-3=-7x-14\\y=-7x-14+3\\y=-7x-11

Therefore, the equation of the line in vertex form is y=-7x-11.

4 0
3 years ago
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