Graphs 2
4 marks · NormalA fitness tracker records the number of steps and the calories burned for four days, as shown in the table below.
| Steps (thousands) | Calories burned |
|---|---|
| 5 | 190 |
| 7 | 266 |
| 9 | 342 |
| 11 | 418 |
Plot a graph of calories burned against steps (thousands) for the four days.
By drawing a straight line through the points, estimate the number of calories burned if 8,000 steps are recorded.
Write down the equation of the line in the form $C = ms + c$, where $C$ is calories burned and $s$ is steps in thousands.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
Show answer
(a) Graph drawn, all 4 points correctly plotted. · must show Correct axes and plotting
(b) 304 cal
(c) C = 38s + 0
Must show: Axes labelled: Steps (thousands), Calories burned, Points plotted correctly
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Plots all points accurately, axes labelled.
A1 (b) · 1 mark · Reads/calculates approximately 304 calories for 8,000 steps (linearly between 266 and 342).
M2 (c) · 1 mark · Correctly uses two points to calculate the gradient.
A2 (c) · 1 mark · Writes a correct linear equation e.g. $C=38s$ (or similar, depending on line drawn).
Worked solution
a) Plot steps on x-axis, calories on y-axis. Points: (5,190), (7,266), (9,342), (11,418).
b) Find increase per 2,000 steps: 342-266=76, so per 1,000 steps = 38. 8,000 steps: 266+38=304.
c) Gradient $m=(266-190)/(7-5)=76/2=38$, intercept $c=190-38\times5=190-190=0$, thus $C=38s$.