Is the relationship shown by the data linear? if so, model the data with an equation. x y 1 –4 7 –7 13 –10 19 –13

Step-by-step

If x and y both go by equal steps, not necessarily equal steps between x and y, the relation is linear

Here, x goes by steps of 6 (1,7,13,19) and y goes by steps of 3 (4,7,10,13), therefore the relation is linear.

To find the equation passing through all the points, we find first the slope, which is steps in y divided by steps in x, or

slope, m = 3/6 = 1/2

Next, we take any point from the data, say, P0=(x0,y0)=(1,4), and substitute in the point-slope form of the equation

y-y0 = m(x-x0)(1)

since x0=1, y0=4, and m=1/2, we get the equation

y-4 = (1/2)*(x-1) (2)

Simplify (2) to get the slope-intercept form of the linear relation:

y = (1/2)x + 7/2 (3)

Finally, we check the results of the y-values for given values of x, using the relation given in equation (3):

y(1) = 4

y(2)=7

y(3)=10

y(4)=13

all of which correspond exactly to original data, so the equation of the linear relation is correct.

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step-by-step explanation: