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3 years ago

Write AN EQUATION of the line that passes through the given points (-1,4) and (2,-5)

1 answer:

7 0

Answer: y = -3x + 1

step-by-step process
find the slope first using (y-y)/(x-x)
(4-(-5))/(-1-2) = 9/(-3)
m = -3

then use one of the points to find the y-intercept by putting it in y=mx+b, substituting m with -3 (aka the slope) as well
4 = -3(-1) + b
4 = 3 + b
4 - 3 = 3 + b - 3
1 = b

therefore, the equation for the line is: y=-3x+1

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A hot air balloon hovers above its launch site at an altitude of 100 meters. The pilot of the balloon sights a parking lot at a

IgorLugansk [536]

Answer:

The horizontal distance between the parking lot and the launch site is 470 meters

Step-by-step explanation:

Let

x-----> the horizontal distance between the parking lot and the launch site

we know that

The tangent of angle of 12 degrees is equal to divide the altitude of 100 meters by the horizontal distance

tan(12°)=100/x

Solve for x

x=100/tan(12°)=470 meters

6 0

2 years ago

there are 12 students who play the clarinet and 16 students who play the viola. what does the ratio 16:12 describe?

Oksi-84 [34.3K]

Answer: The ratio 16:12 describes the ratio of the number of students who play the viola to the students who play the clarinet.

Step-by-step explanation:

Given : Number of students who play the clarinet= 12

Number of students who play the viola=16

We know that ratio of A to B is represented by A:B.

Since, the number '12' is representing " students who play the clarinet" and number '16' is representing " students who play the viola"

So , the ratio 16:12 describes the ratio of the number of students who play the viola to the students who play the clarinet.

6 0

2 years ago

2x+2x-26=114 blank -26=114

Nady [450]

The answer is 35

X= 35

3 0

3 years ago

What is the equation for the line? enter your answer in the box

Igoryamba

To get the equation of the line, you need two points that belong to this line.
From the given graph, we can choose any two points: (0,-4) and (-2,0)

The general for of the linear straight line is:
y = mx + c where m is the slope and c is the y-intercept

First, we will calculate the slope using the following rule:
slope = (y2-y1) / (x2-x1)
slope (m) = (0--4) / (-2-0) = 4/-2 = -2
The equation of the line now is: y = -2x + c

Then, we will get the value of the c. To do so, we will choose any point and substitute in the equation. I will choose the point (0,-4)
y = -2x + c
-4 = -2(0) + c
c = -4

Based on the above calculations, the equation of the line is:
y = -2x - 4

7 0

3 years ago

The yearly cost in dollars, y, at a video game arcade based on total game tokens purchased, x, is y = x + 60 for a member and y

morpeh [17]

We have the yearly cost in dollars y at a video game arcade based on total game tokens purchased $x$ . So we know that:

 $y=x+60:\ equation \ for \ a \ member$ 

 $y=x:\ equation \ for \ a \ nonmember$ 

Then we can study this problem by using the graph in the figure below. We know that if there's no any purchase, the yearly cost for a member will be $60 and for a nonmember there will not be any cost. From this, we can affirm that the cost of membership is equal to $60.

On the other hand, both members and nonmembers will pay the same price on the total game tokens purchased, this is true because of the same slope that members and nonmembers have in the equations.

8 0

2 years ago

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