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Is the relationship shown by the data linear? If so, model the data with an equation. x y –7 5 –5 9 –3 13 –1 17

User Sixones
by
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1 Answer

7 votes

Given:

The table of values is:

x : -7 -5 -3 -1

y : 5 9 13 17

To find:

Whether the given data is linear and then find the equation.

Solution:

The given data is linear if the slope and rate of change is constant.

Slope formula:


m=(y_2-y_1)/(x_2-x_1)

Using the slope formula. we get


(9-5)/(-5-(-7))=2


(13-9)/(-3-(-5))=2


(17-13)/(-1-(-3))=2

Since the rate of change is constant, i.e., 2, therefore the given data is linear.

The slope of a linear equation is 2 and it passes through the point (-7,5). So, the equation of the line is:


y-y_1=m(x-x_1)


y-5=2(x-(-7))


y-5=2(x+7)


y-5=2x+14

Adding 5 on both sides, we get


y-5+5=2x+14+5


y=2x+19

Therefore, the equation for the given data is
y=2x+19.

User Akshar
by
6.3k points
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