Question Type 2: Graphing different linear models Exercises

A car loses value linearly from $$20000$ to $$8000$ over 5 years. Find its value $V(t)$ after $t$ years and sketch the depreciation curve for $0\le t\le5$.

A factory has a fixed daily cost of $500$ and a variable cost of $3$ per unit produced. If each unit sells for $8$, find the break-even production level and sketch cost and revenue lines on the same axes.

A water tank is filling such that the depth increases linearly from $0$ cm to $12$ cm in $4$ minutes.

Find the depth $d(t)$ after $t$ minutes, and sketch the graph for $0 \le t \le 4$.

A cyclist travels at a constant speed of $15 \text{ km h}^{-1}$. Express the distance $s$ in km as a function of time $t$ in hours, then graph $s(t)$ for $0 \le t \le 3$.

A crop yield $Y$ ($\text{kg/ha}$) increases linearly with fertilizer amount $f$ ($\text{kg/ha}$): $Y=2f+50$. Predict the yield at $f=30 \text{ kg/ha}$ and sketch the line for $0\le f\le100$.

Sketch the graph of the linear function $y = 2x + 3$. Label the $x$- and $y$-intercepts.

Plan A: $20 monthly plus $0.15 per minute of calls. Plan B: $5 monthly plus $0.30 per minute. Determine the number of call minutes $m$ where the two plans cost the same, and indicate which plan is cheaper for $m<100$.

A taxi service charges a base fare of $4 plus $2.50 per kilometre. Write the cost $C$ as a function of distance $d$ in kilometres, then graph $C(d)$ for $0\le d\le10$.

Determine the equation of the line passing through the points $(1,4)$ and $(3,10)$, then sketch its graph.

The relationship between temperature in Celsius ($T_C$) and Fahrenheit ($T_F$) is given by $T_F = 1.8T_C + 32$.

Sketch the graph of this relationship for $-20 \le T_C \le 40$.

Two shipping companies charge as follows for packages weighing $w$ kg:

Company $X: 5 + 1.20w$ Company $Y: 3 + 1.50w$

(a) Determine for which weights Company $X$ is cheaper.

(b) Sketch both cost functions on the same axes for $0 \le w \le 20$.

A mobile data plan costs $15 plus $0.10 per megabyte used. Express total cost $T$ in dollars as a function of data usage $x$ in MB, then find $T$ when $x=200$ MB and sketch the graph.