Question

Y=3x-2

A)
Is the ordered pair (3, 7) a solution of the equation? (1point)

B) What is the rate of change of the equation? (1 point)

C) What is the y-intercept of the equation? (1 point)

D) Make up a real-world scenario that would go with this equation. (2 points)

Answer 1

a)
`(x,y) = (3, 7)` is a solution of the linear equation.

b) The rate of change of the equation is 3.

c) The y-intercept of the equation is -2.

d) Jayne is working in the grocery one day, according to her calculations, renting the lot costs 2 dollars per day and she could earn 3 dollars per hour by selling pastries. How much money does she earn after working 8 hours?

Explanation:

a) If
`(x,y) = (3, 7)` is a solution of the linear equation, then
`f(3) = 7`. If
`x = 3`, then the function evaluated at this value is:

`y = 3\cdot (3) -2`

`y = 7`

Hence,
`(x,y) = (3, 7)` is a solution of the linear equation.

b) The rate of change of the equation is represented by the slope of the function, which is the constant that multiplies the indepedent variable (
`x`). Hence, the rate of change of the equation is 3.

c) The y-intercept of the equation is the only constant of the equation. Hence, the y-intercept of the equation is -2.

d) A real-world scenario would be the following: Jayne is working in the grocery one day, according to her calculations, renting the lot costs 2 dollars per day and she could earn 3 dollars per hour by selling pastries. How much money does she earn after working 8 hours?