Question

Is the relationship shown by the data linear? If so, model the data with an equation. x y

–9,–2
–5,–7
–1,–12
3,–17

Answer 1

Yes, the given relationship shown by the data is linear, as the values of x variables vary with a difference of 4 and all the values of y variables vary with a difference of -5.

The slope(m) of for the points
`(x_(1),y_(1)) and (x_(2),y_(2))` is given by
`((y_(2)-y_(1)) )/((x_(2)-x_(1)))`

Slope for points (-9,-2) and (-5,-7) is

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

=
`(-5 )/(4)`

Equation is given by:
`(y-y_(1))= m(x-x_(1))`

`4y+5x=-53` which is a linear equation.

The model of the given linear equation is attached.