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

$y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)$

$y-(-2)=\dfrac{5.7-(-2)}{6-(-5)}(x-(-5))$

$y+2=\dfrac{5.7+2}{6+5}(x+5)$

$y+2=\dfrac{7.7}{11}(x+5)$

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

$y+2=0.7x+3.5$

Subtract 2 from both sides.

$y=0.7x+3.5-2$

$y=0.7x+1.5$

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

Answer 2

Answer:

A

Step-by-step explanation: