Question

Which statement best compares the slopes and y intercepts of the two functions Function 1 has a greater slope and greater y-intercept than Function 2.Function 2 has a greater slope and greater y-intercept than Function 1.Function 1 has a greater slope and leşser y-intercept than Function 2. Function 2 has a greater slope and lesser y-intercept than Function 1.

Answer 1

From function 1:

`\begin{gathered} y=(1)/(3)x+2 \\ m=\text{slope}=(1)/(3) \\ b=y-\text{intercept}=2 \end{gathered}`

For function 2:

`\begin{gathered} (x1,y1)=(-3,-3) \\ (x2,y2)=(3,0) \\ m=(0-(-3))/(3-(-3))=(3)/(6)=(1)/(2) \\ \text{ Using the point slope equation:} \\ y-y1=m(x-x1) \\ y+3=(1)/(2)(x+3) \\ y=(1)/(2)x+(3)/(2) \\ y=(1)/(2)x-(3)/(2) \end{gathered}`

Therefore: Function 2 has a greater slope and lesser y-intercept than Function 1.