Explanation
the function for the distance is given by
[tex]\text{distance}=\text{ sp}eed\cdot time\text{ }[/tex]then, let
speed= 0.25 m/s
time= t
distance= 2m
hence, replace
[tex]\begin{gathered} \text{distance}=\text{ sp}eed\cdot time\text{ } \\ \text{distance}=0.25\frac{m}{s}\cdot t \\ d(t)=0.25t\Rightarrow equation\text{ of the line} \end{gathered}[/tex]Step 2
now, to graph the line we need 2 points
a) when t= 0
[tex]\begin{gathered} d(t)=0.25t\Rightarrow equation\text{ of the line} \\ d(0)=0.25\cdot0 \\ d(0)=0 \\ so \\ \text{coordinate 1(0,0)} \end{gathered}[/tex]P1(0,0)
b) when the car has covered 2m
let d=2
replace and solve for x
[tex]\begin{gathered} d(t)=0.25t\Rightarrow equation\text{ of the line} \\ 2=0.25t \\ \text{divide both sides by 0.25} \\ \frac{2}{0.25}=\frac{0.25t}{0.25} \\ 8=t \\ \text{hence, after 8 seconds, the distance is 2 m, so the coordinate is} \\ (8,2) \end{gathered}[/tex]P2(8,2)
finally, draw a line that passes through the point P1(0,0) and P2(8,2)
I hope this helps you
