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iogann1982 [59]
3 years ago
8

Amanda placed her finger on the origin of a regular coordinate plane. She marked a point after moving her finger 1 unit to the l

eft and 5 units down. What is the order pair of the point that Amanda marked?
Mathematics
1 answer:
Lubov Fominskaja [6]3 years ago
3 0

Answer:

( x , y ) = ( -1 , - 5 )

Step-by-step explanation:

Solution:-

- The rectangular coordinate system ( Cartesian ) is defined by two independent variables namely, "x and y".

- The values of both varibales lie on the horizontal and vertical line respectively, ( x & y ).

- The values on the horizontal axis also known as the x-axis is marked with a referece of x = 0 ( origin ). All the values to the right of the point of origin are denoted as positive units and all values to the left of the point of origin are denoted as negative units.

- Similarly, The values on the vertical axis also known as the y-axis is marked with a referece of y = 0 ( origin ). All the values to the above the point of origin are denoted as positive units and all values below of the point of origin are denoted as negative units.

- The axis are conventionally oriented such that 90 degrees angle is formed in between them and always denoted in the counter-clockwise direction.

In other words, if +x is pointing to the right then the +y will be pointed in the direction when +x is rotated counter clockwise to 90 degrees; hence, points upward.

- When Amanda starts off at the origin she is at the order pair  ( 0 , 0 ).

- She then moves her finger 1 unit to left ( -x ) and 5 units down ( -y ). Hence, she moves 1 unit along the -x direction and then moves 5 units down along -y direction.

Hence, she is at an ordered pair ( x , y ) = ( -1 , - 5 ) .

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Conclusion:

The rate of change of function 1  = 3

The rate of change of function 2 = 5/3

  • Hence, function 1 has a greater rate of change

The initial Value of function 1 = y = 2

The initial Value of function 2 = y = 3

  • Hence, function 2 has a greater initial value.

Step-by-step explanation:

Function 1)

Determining rate of change for function 1:

x        1         2         3         4

y       5        8          11        14

Finding the rate of change or slope using the formula

Rate of change = m = [y₂-y₁] / [x₂-x₁]

Taking any two points, let say (1, 5) and (2, 8)

Rate of change = m = [8-5] / [2-1]

                                 = 3/1

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Therefor, the rate of change of function 1 = m = 3

using point-slope form to determine the function equation

y-y₁ = m (x-x₁)

where m is the rate of change or slope

substititng m = 3 and the point (1, 5)

y - 5 = 3(x - 1)

y - 5 = 3x-3

y = 3x-3+5

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Thus, equation of function 1 will be:

y = 3x + 2

Determining Initial Value for Function 1:

substituting x = 0 in the equation to determine the initial value

y = 3(0)+2

y = 0+2

y = 2

Therefore, the initial Value of function 1 will be: y = 2

Function 2)

Determining the rate of change for function 2:

Given the function 2

y\:=\:\frac{5}{3}x+3

comparing with the slope-intercept form of a linear function

y = mx+b     where m is the rate of change

so the rate of change of function 2 = m = 5/3

Determining Initial Value for Function 2:

substituting x = 0 in the equation to determine the initial value

y\:=\:\frac{5}{3}x+3

y\:=\:\frac{5}{3}\left(0\right)+3

y = 0+3

y = 3

Therefore, the initial Value of function 2 will be: y = 3

Conclusion:

The rate of change of function 1  = 3

The rate of change of function 2 = 5/3

  • Hence, function 1 has a greater rate of change

The initial Value of function 1 = y = 2

The initial Value of function 2 = y = 3

  • Hence, function 2 has a greater initial value.

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