Question

The value of the function g(x) is −2 when x=−5 and is 5.7 when x=6. What is the equation for the function g(x)?(1 point)

Answer 1

Given:

The value of the function g(x) is −2 when x=−5 and is 5.7 when x=6.

To find:

The equation of the function.

Solution:

The value of the function g(x) is −2 when x=−5. It means the graph of function passes through (-5,-2).

The value of the function g(x) is 5.7 when x=6. It means the graph of function passes through (6,5.7).

The equation of function g(x) that passes through (-5,-2) and (6,5.7) is

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

`y-(-2)=(5.7-(-2))/(6-(-5))(x-(-5))`

`y+2=(5.7+2)/(6+5)(x+5)`

`y+2=(7.7)/(11)(x+5)`

`y+2=0.7(x+5)`

`y+2=0.7x+3.5`

Subtract 2 from both sides.

`y=0.7x+3.5-2`

`y=0.7x+1.5`

Therefore, the equation of function g(x) is
`y=0.7x+1.5`.