Solution
Step 1
Given data
Rate of change = -3.2
Given point = (-3,-2)
Step 2
Using the rate of change formula
[tex]Rate\text{ of change = }\frac{y-y_1}{x-x_1}[/tex]
Step 3
Substitute into the formula
[tex]\begin{gathered} -3.2\text{ = }\frac{y-(-2)}{x-(-3)} \\ \\ -3.2\text{ = }\frac{y+2}{x+3} \\ \\ y+2\text{ = -3.2\lparen x+3\rparen} \\ \\ y+2\text{ = -3.2x + 3}\times(-3.2) \\ \\ y+2\text{ = -3.2x - 9.6} \\ \\ y\text{ = -3.2x-9.6-2} \\ \\ y\text{ = -3.2x - 11.6} \end{gathered}[/tex]
a) the formula for the linear function is: y = -3.2x - 11.6
b)
[tex]\begin{gathered} y\text{ = -3.2x - 11.6} \\ \\ Substitute\text{ x = 5 to find y.} \\ \\ y=-3.2\times5-11.6 \\ \\ y\text{ = -16-11.6} \\ \\ y\text{ = -27.6} \end{gathered}[/tex]
