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gizmo_the_mogwai [7]
3 years ago
5

What is the value of y?Exaplain what the coordinates repersent

Mathematics
1 answer:
FinnZ [79.3K]3 years ago
5 0

Answer:

(1, 35) means that $35 is the cost per hour of hiring a face painter.

Step-by-step explanation:

Notice that this is a linear function that goes through the origin and also through the point (5, 175) which according to the data plotted in both axis, means that for 5 hours of service, the cost is $175.

One can calculate the slope of this line as that of the segment that joins (0, 0) with (5, 175) as:

slope = (175 - 0) / (5 - 0) = 175 / 5 = 35 / 1

Notice as well that such slope reads the amount of dollars to hire a face painter for ONE hour (so it is the rate per hour for hiring a face painter).

So the point (1 , y) should be completed as: (1, 35) and means "the rate per hour for hiring a face painter."

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3 years ago
Line segment GT contains the point G(−3, 5) and a midpoint at A(1, −4). What is the location of endpoint T?
algol [13]

Imagine you're moving along the segment. Since the midpoint is in the middle of the segment (obviously), it means that when you've traveled from G to A, you're halfway through your journey, along both x and y directions. So, let's break the problem in two and analyze both directions.


Along the x axis, you've moved from -3 to 1, so you moved 4 units forward. This means that you have 4 units still to go, and your journey will end at coordinate 5.


Similarly, along the y axis, you've moved from 5 to -4, so you moved 9 units downward. This means that you have 9 units still to go, and your journey will end at coordinate -13.


So, the coordinates of the endpoint are T = (5,-13)


If you prefer a more analyitical approach, simply write the definition of the midpoint and solve it for the coordinates of T.


We have G = (-3, 5) and T = (x_T,y_T). The midpoint is computed as


A = \left( \frac{-3+x_T}{2},\frac{5+y_T}{2} \right) = (1, -4)


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\frac{-3+x_T}{2} = 1,\qquad \frac{5+y_T}{2} = -4


Multply both equations by 2 to get


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Move the constants to the right hand sides to get


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