Question

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

Answer 1

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:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

Using the slope formula. we get

$\dfrac{9-5}{-5-(-7)}=2$

$\dfrac{13-9}{-3-(-5)}=2$

$\dfrac{17-13}{-1-(-3)}=2$

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 $y=2x+19$.