Question

8. * The functions f(x) and g(x) are both linear. f(2) = 4 and f(3) = -1, while g(2) = 6 and g(-3) = 7. Are these lines parallel, perpendicular, or neither? Show your work algebraically. 9. ** f(x) = 5x – 2 and g(x) = 2x + 4. Are f(x) and g(x) parallel, perpendicular or neither parallel nor perpendicular to each other. Justify.

Answer 1

`\begin{gathered} \text{for the line f we have 2 points:} \\ (x_1,y_1)=(2,4) \\ \text{and} \\ (x_2,y_2)=(3,-1) \\ \text{hence, the slope} \\ m=(y_2-y_1)/(x_2-x_1) \\ is\text{ given by} \\ m=(-1-4)/(3-2) \\ m=-(5)/(1) \\ m=-5 \\ \text{now we ne}ed\text{ to find the slope for g} \end{gathered}`
`\begin{gathered} \text{For g we have 2 points:} \\ (x_1,y_1)=(2,6) \\ (x_2,y_2)=(-3,7) \\ \text{hence, the slope is given by} \\ m=(7-6)/(-3-2) \\ m=(1)/(-5) \end{gathered}`
`\begin{gathered} \text{parallel lines has the same slope.} \\ \text{perpendicular lines has reciprocal negative slope}\colon \\ m\Rightarrow-(1)/(m) \\ IN\text{ THIS CASE, they are neither parallel nor perpendicular since} \\ m=-5 \\ \text{and} \\ m=-(1)/(5) \\ \text{are not perpendicular } \end{gathered}`