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:

$\begin{gathered} y=\frac{1}{3}x+2 \\ m=\text{slope}=\frac{1}{3} \\ b=y-\text{intercept}=2 \end{gathered}$

For function 2:

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

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