1.2P: Practice

Exercise

Earl the squirrel has only ten more days until hibernation. He needs to save 50 more acorns. He is tired of collecting acorns and so he is only able to gather 8 acorns every 2 days.

a) Let \(t\) represent time in days (independent variable). Let \(N\) represent the number of acorns collected (dependent variable). Set up an appropriately scaled coordinate system on graph paper.

b) At time \(t = 0\), Earl has collected zero of the acorns he needs. To what point does this correspond? Plot this point.

c) After two days (\(t = 2\)), Earl has collected 8 acorns. Move 2 days to the right and 8 acorns up. Plot this point. What are its coordinates?

d) Continue plotting every 2 days, adding 8 acorns, until you reach 14 days.

e) Treating the situation as continuous, draw a line through your data points.

f) Use the graph to determine how many acorns Earl will have collected after 10 days. Will it be enough?

g) Convert the rate of 8 acorns every 2 days to a unit rate of acorns per day.

h) Fill in the missing entries in the table below.

i) Write a linear equation that represents \(N\), the number of acorns collected after \(t\) days.

j) Use your equation to predict the number of acorns after 10 days. Does this agree with your graph in part (f)?

Exercise

Set up a coordinate system on a sheet of graph paper, plotting the points \(P(-1, 3)\) and \(Q(5, -3)\) and drawing the line through them.

a) What can you say about the slope of the line?

b) Find the slope of the line.

c) Find the equation of this line.

Exercise

Find the equation of the line graphed below.

Exercise

The following coordinate system shows the graphs of three lines. Match each slope:

slope \(= 1\)

slope \(= \frac{2}{3}\)

slope \(= -2\)

Exercise

Draw a line through the point \(P(1, 3)\) that is parallel to the line through the origin and the point \((4,-1)\). Then find the equation of both lines.

Exercise

Draw a coordinate system from \(-10\) to \(10\) on both axes.

a) Draw a line through \((-1, -2)\) with slope \(\frac{3}{4}\)

b) Draw another through \((0, 1)\) with slope \(\frac{4}{3}\)

c) Are they parallel, perpendicular, or neither?

Exercise

When construction crews talk about the grade of a road, it is equivalent to slope but written as a percentage. For example a slope of 1/4 could be written as a grade of 25%.

a) Express 8% grade as slope

b) Hill drops 16 ft over 180 ft — what is the grade?

c) What does 0% grade mean?