Question

The ordered pairs (3,2) and (-2,13) are points on a linear function. Which equation best describes this function?

Answer 1

Answer:

The equation which describe this function is 5x + 11y = 37

Step-by-step explanation:

To find the slope

slope = (y₂ - y₁)/(x₂ - x₁)

slope = (13 - 2)/(-2 - 3) = 11/-5

To find the equation

(x - 3)/(y - 2) = -11/5

5(x - 3) = -11(y - 2)

5x -15  = -11y + 22

5x + 11y = 22 + 15

5x + 11y = 37

Therefore the equation which describe this function is

5x + 11y = 37

Answer 2

Answer:

y = $\frac{-11}{5}$ x + $\frac{43}{5}$

Step-by-step explanation:

Linear function is defined by  y = ax+b

         where a and b are constants and (x,y ) are variables given as point

using point (3,2) that is plugging x =3 and y =2 ,we

                      2 = 3a+b .............  equation(1)

  likewise using point (-2,13) and plugging x =-2 and y =13 ,we get

                  13 = -2a+b ..........  equation(2)

      Solving the equation   (1) and 2

          $\left \{ {{2=3a+b} \atop {13=-2a+b}} \right.$

          subtracting equation 2 from equation 1

             3a+b = 2

             -2a+b = 13

__-_______________

         we have  5a =  -11

                          a= $\frac{-11}{5}$

plugging a=$\frac{-11}{5}$ in equation (1),we get

3($\frac{-11}{5}$) +b =2

b =  2 -3($\frac{-11}{5}$)

b = 2+$\frac{33}{5}$

b=$\frac{43}{5}$

therefore equation is obtained by plugging

 a =$\frac{-11}{5}$ and b = $\frac{43}{5}$

we get  equation as

    y = $\frac{-11}{5}$ x + $\frac{43}{5}$