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MissTica
3 years ago
8

What is the equation of a line that passes through the points (-3, 4) and (2,8)?

Mathematics
1 answer:
ziro4ka [17]3 years ago
6 0

Given that the line passes through the two points (-3,4) and (2,8)

We need to determine the equation of the line.

<u>Slope:</u>

The slope of the line can be determined using the formula,

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

Substituting the points (-3,4) and (2,8) in the above formula, we get;

m=\frac{8-4}{2+3}

m=\frac{4}{5}

Thus, the slope of the line is m=\frac{4}{5}

<u>Equation of the line:</u>

The equation of the line can be determined using the formula,

y-y_1=m(x-x_1)

Substituting the point (-3,4) and m=\frac{4}{5} in the above formula, we have;

y-4=\frac{4}{5}(x+3)

y-4=\frac{4}{5}x+\frac{12}{5}

     y=\frac{4}{5}x+\frac{12}{5}+4

     y=\frac{4}{5}x+\frac{32}{5}

Thus, the equation of the line is y=\frac{4}{5}x+\frac{32}{5}

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Consider the function f(x)=−5x−8 and find the following: a) The average rate of change between the points (−1,f(−1)) and (3,f(3)
kipiarov [429]

Answer:

a. -5

b.-5

c.-5

Step-by-step explanation:

In order to find the average rate of change of a function , we divide the change in the output value by the change in the input value.

Generally, the average rate of change (ARC) on an ecuatios  between two points (x1,f(x1)) and (x2,f(x2)) is

  • ARC = [f(x2)-f(x1)]/ (x2-x1)

<em>In case a)</em>

f(-1)= -5*(-1)-8=5-8= -3          f(3)= -5*3-8= -23

Then ARC= (-23-(-3))/(3-(-1))=-20/4=-5

<em>In case b)</em>

f(a)= (-5a-8)

f(b)= (-5b-8)

Then ARC= [(-5b-8)-(-5a-8)]/(b-a)= (-5b+5a)/(b-a)= -5(b-a)/(b-a)= -5

<em>In case c)</em>

f(x)= -5x-8

f(x+h)= -5(x+h)-8= -5x-5h-8

then ARC= [(-5x-5h-8)-(-5x-8)]/(x+h-x) =-5h/h= -5

3 0
3 years ago
The point-slope form of the equation of a line that passes through points (8, 4) and (0, 2) is
Sladkaya [172]

Answer:

y= x-4

Step-by-step explanation:

5 0
3 years ago
Points giveaway<br><br>2+3=?​
Nata [24]

Answer:

5

Step-by-step explanation:

  • 2+3
  • 5

Hence it is correct.. thanks for points.

5 0
2 years ago
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Sam needs to make a long-distance call from a pay phone. With his prepaid phone card, he will be charged $1.00 to connect and $0
Mademuasel [1]

Answer:  The required system of equations representing the given situation is

y=1+0.5x\\\\y=3+0.25x

Step-by-step explanation: Given that Sam needs to make a long-distance call from a pay phone.

We are to write a system to represent the situation.

Let x represent the number of minutes Sam talked on the phone and y represents the total amount that he paid for the call.

According to the given information,

with prepaid phone card, Sam will be charged $1.00 to connect and $0.50 per minute.

So, the equation representing this situation is

y=1+0.5x~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)

Also, if Sam places a collect call with the operator he will be charged $3.00 to connect and $0.25 per minute.

So, the equation representing this situation is

y=3+0.25x~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)

Thus, the required system of equations representing the given situation is

y=1+0.5x\\\\y=3+0.25x

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