4.2 Modeling with linear functions  (Page 6/9)

Explain how to find the input variable in a word problem that uses a linear function.

Explain how to find the output variable in a word problem that uses a linear function.

Explain how to interpret the initial value in a word problem that uses a linear function.

Explain how to determine the slope in a word problem that uses a linear function.

Find the area of a parallelogram bounded by the y -axis, the line $x=3,$ the line $f(x)=1+2x,$ and the line parallel to $f(x)$ passing through $\left(\text{2},\text{7}\right).$

Find the area of a triangle bounded by the x -axis, the line $f(x)=12–\frac{1}{3}x,$ and the line perpendicular to $f(x)$ that passes through the origin.

Find the area of a triangle bounded by the y -axis, the line $f(x)=9–\frac{6}{7}x,$ and the line perpendicular to $f(x)$ that passes through the origin.

Find the area of a parallelogram bounded by the x -axis, the line $g(x)=2,$ the line $f(x)=3x,$ and the line parallel to $f(x)$ passing through $(6,1).$

Predict the population in 2016.

Identify the year in which the population will reach 0.

Predict the population in 2016.

Identify the year in which the population will reach 75,000.

Find the linear function that models the town’s population $P$ as a function of the year, $t,$ where $t$ is the number of years since the model began.

Find a reasonable domain and range for the function $P.$

If the function $P$ is graphed, find and interpret the x - and y -intercepts.