Question Type 2: Graphing different linear models Exercises

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

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

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.

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

A water tank is filling at a rate that increases depth from 0 to 12 cm in 4 minutes linearly. Find the depth $d(t)$ after $t$ minutes, then draw the graph for $0\le t\le4$.

Convert the temperature $T_C$ in Celsius to $T_F$ in Fahrenheit using the linear relation $T_F=1.8T_C+32$. Graph this relation for $-20\le T_C\le40$.

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 cyclist travels at a constant speed of $15$ km/h. Express the distance $s$ in km as a function of time $t$ in hours, then graph $s(t)$ for $0\le t\le3$.

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

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 $m<100$.

Two shipping companies charge as follows for packages weighing $w$ kg: Company $X: 5+1.20w$; Company $Y:3+1.50w$. Determine for which weights Company $X$ is cheaper, and sketch both cost functions on $0\le w\le20$.