Subjects algebra

Car Distance Time 1F5Cee

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1. **State the problem:** We are given time and distance data for a car moving north and asked to create a line graph representing this data. 2. **Identify variables:** The independent variable is time $t$ in seconds (x-axis), and the dependent variable is distance $d$ in units (y-axis). 3. **Data points:** The points are $(0,0)$, $(1,2)$, $(2,4)$, $(3,6)$, $(4,8)$, and $(5,10)$. 4. **Determine the relationship:** Notice the distance increases by 2 units every second, indicating a linear relationship. 5. **Find the equation of the line:** The slope $m$ is change in distance over change in time: $$m=\frac{10-0}{5-0}=\frac{10}{5}=2$$ The line passes through the origin, so the equation is: $$d=2t$$ 6. **Plotting instructions:** - Label x-axis as "Time (s)" and y-axis as "Distance (units)". - Use equal intervals on both axes. - Plot the points and connect them with a straight line. - Add a title such as "Car Distance vs Time". This line graph visually shows the car's constant speed of 2 units per second northward. **Final answer:** The linear function describing the data is $$d=2t$$.