Find the linear function represented by the graph.The slope of the line isThe y-intercept of the line is at 3What linear function is represented by the graph?

Accepted Solution

Answer:Slope is [tex]\frac{1}{3}[/tex]Good job on the y-intercept![tex]f(x)=\frac{1}{3}x+3[/tex] is function represented here.Step-by-step explanation:The slope is [tex]\frac{\text{rise}}{\text{run}}[/tex].Let's start at the left dot on your screen; we are going to figure out how to get to (0,3) only using up, down,right, left.So since the slope is [tex]\frac{\text{rise}}{\text{run}}[/tex] and we are starting at the left dot trying to get to right, let's find the rise part first.  How much would you need to rise to get on the same level as that dot on the right? You should say the rise is positive 1 (since you go up 1).Now that we are on the level, what would you need to run from left to right to get to the right dot.  The run is positive 3 (since we went right 3).So the slope is  [tex]\frac{\text{rise}}{\text{run}}=\frac{1}{3}[/tex]You did good on the y-intercept! Good job!The slope-intercept form a line is y=mx+b where m is the slope and b is the y-intercept.[tex]m=\frac{1}{3}[/tex] and [tex]b=3[/tex]Plug this in:[tex]y=\frac{1}{3}x+3[/tex]