Question

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

Answer 1

y =
`(-11)/(5)` x +
`(43)/(5)`

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=
`(-11)/(5)`

plugging a=
`(-11)/(5)` in equation (1),we get

3(
`(-11)/(5)`) +b =2

b = 2 -3(
`(-11)/(5)`)

b = 2+
`(33)/(5)`

b=
`(43)/(5)`

therefore equation is obtained by plugging

a =
`(-11)/(5)` and b =
`(43)/(5)`

we get equation as

y =
`(-11)/(5)` x +
`(43)/(5)`

Answer 2

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

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