Chapter 11: Review

The chapter problem, solved

The walker travels 2 km in 30 minutes. At a constant rate, the distance doubles when the time doubles:

The walker is 4 km from home after one hour. To draw the journey, plot time on the horizontal axis and distance from home on the vertical axis. Use the points $(0,0)$ and $(30,2)$, then draw the straight line that models a constant speed. Its gradient is $2/30=1/15$ km per minute.

Mixed practice: choose a method

For each item, name the graph method you will use and explain why before calculating. Questions marked H are Higher only.

1. Plot $(-2,3)$ and $(4,-1)$. Which coordinate gives the horizontal position?
2. Work out the gradient between $(1,4)$ and $(5,12)$.
3. State the gradient and $y$-intercept of $y=-3x+7$.
4. Find the equation of the line with gradient $2$ through $(0,-1)$.
5. H Give the gradient of a line perpendicular to $y=4x+2$.
6. A distance-time graph rises 15 km in 0.5 hours. Find the speed in km/h.
7. H A velocity-time graph has velocity 6 m/s for 5 seconds. Find the area under the graph and explain what it represents.
8. Which has greater gradient: the line through $(0,1),(3,7)$ or the line through $(0,0),(2,5)$? Give a reason.

What you can now do

• plot and interpret coordinates and straight-line graphs;
• find gradient and intercept, then use them to write line equations;
• compare parallel and perpendicular lines;
• read rates from real-life graphs and interpret area under a graph.

Your reflection

Return to your example from the chapter opener. What could the graph help you predict or compare? Write one thing you can now explain using a graph.