Question

Would you mind sending me the way to solve #54

Answer 1

Step 1

Given data

Rate of change = -3.2

Given point = (-3,-2)

Step 2

Using the rate of change formula

`Rate\text{ of change = }(y-y_1)/(x-x_1)`

Step 3

Substitute into the formula

`\begin{gathered} -3.2\text{ = }(y-(-2))/(x-(-3)) \\ \\ -3.2\text{ = }(y+2)/(x+3) \\ \\ y+2\text{ = -3.2\lparen x+3\rparen} \\ \\ y+2\text{ = -3.2x + 3}*(-3.2) \\ \\ y+2\text{ = -3.2x - 9.6} \\ \\ y\text{ = -3.2x-9.6-2} \\ \\ y\text{ = -3.2x - 11.6} \end{gathered}`

a) the formula for the linear function is: y = -3.2x - 11.6

b)

`\begin{gathered} y\text{ = -3.2x - 11.6} \\ \\ Substitute\text{ x = 5 to find y.} \\ \\ y=-3.2*5-11.6 \\ \\ y\text{ = -16-11.6} \\ \\ y\text{ = -27.6} \end{gathered}`