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trasher [3.6K]
3 years ago
13

Write the slope-intercept form of the line passing through (–8, –5) and (4, 4).

Mathematics
2 answers:
Alja [10]3 years ago
6 0

Answer:

\huge\boxed{y = \frac{3}{4}x+1}

Step-by-step explanation:

<u>Finding the slope (m) first:</u>

Given the coordinates (-8 , -5) and ( 4 , 4 )

Slope = \sf \frac{Rise}{Run}

Slope = \sf \frac{y2-y1}{x2-x1}

Slope = \frac{4 + 8}{4+5}

Slope = \frac{12}{9}

Slope = m = \frac{3}{4}

<u>Finding y - intercept (b) :</u>

Taking a coordinate say (4,4)

And putting it in slope intercept form along with b

y = mx+b

Where y = 4 , m = 3/4 and x = 4

4 = (3/4)(4) + b

4 = 3+b

4-3 = b

1 = b

So,

b = 1

<u>Putting m and b now in slope-intercept equation:</u>

y = mx+b

y = \frac{3}{4}x+1

lawyer [7]3 years ago
4 0

Answer:

\Huge \boxed{y=\frac{3}{4} x+1}

\rule[225]{225}{2}

Step-by-step explanation:

We can find the slope through two points.

m = (y2 - y1)/(x2 - x1)

m = (4 - -5)/(4 - -8)

m = 9/12 = 3/4

The slope of the line is 3/4.

Slope-intercept form of a line is y=mx+b. Where m is the slope and b is the y-intercept.

y = 3/4x + b

A point on the line is (4, 4). x = 4 and y =4.

4 = 3/4(4) + b

4 = 3 + b

b = 1

The y-intercept is 1.

\rule[225]{225}{2}

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Is the following statement correct? Explain.
Maksim231197 [3]

Answer:  The answer is NO.


Step-by-step explanation: The given statement is -

If the graph of two equations are coincident lines, then that system of equations will have no solution.

We are to check whether the above statement is correct or not.

Any two equations having graphs as coincident lines are of the form -

ax+by=c,\\\\dax+dby=dc,\\\\\textup{where}~~d\neq 1.

If we take d = 1, then both the equations will be same.

Now, subtracting the second equation from first, we have

a(1-d)x+b(1-d)y=c(1-d)\\\\\Rightarrow ax+by=c,~\textup{since}~d\neq 1,~\textup{so}~1-d\neq 0.

Again, we will get the first equation, which is linear in two unknown variables. So, the system will have infinite number of solutions, which consists of the points lying on the line.

For example, see the attached figure, the graphs of following two equations is drawn and they are coincident. Also, the result is again the same straight line which has infinite number of points on it. These points makes the solution for the following system.

2x+5y=10,\\\\6x+15y=30.

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4 0
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For how many movies is the cost of the plans the same?
sesenic [268]

Answer:

For 36 movies the cost of both the plans is same.

Step-by-step explanation:

Let us assume foe m movies, both the plans cost same.

Now, PLAN A:

Annual Fee = $45

Cost per movie  =  $2.50

⇒The cost of watching m movies  = m x (Cost of 1 movie)

= m x ($2.50) = 2.5  m

So, the total cost of Plan  A  = Annual Fee + Cost of m moves

                                                 = 45 + 2.50 m

PLAN B:

Cost per movie  =  $3.75

⇒The cost of watching m movies  = m x (Cost of 1 movie)

= m x ($3.75) = 3.75  m

ACCORDING TO QUESTION:

for m movies,  Cost of plan A = Cost of plan B

⇒45 + 2.50 m  = 3.75  m

or, 3.75 m  - 2.5 m = 45

or, m  = 45/1.25 = 36

or, m  = 36

Hence, for 36 movies the  cost of  both the plans is same.

5 0
3 years ago
Give an example of each of the following:
Igoryamba

Part a.

The function f(x) = sqrt(x-1) has the domain [1, infinity). We would solve x-1 >= 0 for x to get x >= 1 to ensure that the (x-1) expression is never negative. So the smallest x value we can plug in is x = 1. Recall that applying the square root to a negative number is not defined (assuming you are ignoring complex or imaginary numbers).

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Part b.

Pick any number you want. Then add on some other number. Let's say we pick 7 as our first number. Then let's say we add on 4. That gets us to 11. Add on 4 again and we jump up to 15. Do it again twice more and you have this sequence

7, 11, 15, 19, 23

which is arithmetic since we increase by the same amount (4) each time. The first term is 7 and the common difference is 4.

--------------------------------------------------------

Part c.

There are lot of options here. All we need to do is ensure that the slopes of each line are different. This will guarantee that the lines are not parallel. Non-parallel lines will always cross each other one time and one time only.

So one system we could have is

\begin{cases}y = 2x+3 \\ y = 6x-7\end{cases}

the slopes 2 and 6 are different so the system will have exactly one solution.

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