일차함수와 그래프

A city’s population in the year 1960 was 287,500. In 1989 the population was 275,900. Compute the rate of growth of the population and make a statement about the population rate of change in people per year.

A town’s population has been growing linearly. In 2003, the population was 45,000, and the population has been growing by 1,700 people each year. Write an equation, $P(t),$ for the population $t$ years after 2003.

Suppose that average annual income (in dollars) for the years 1990 through 1999 is given by the linear function: $I(x)=1054x+23,286,$ where $x$ is the number of years after 1990. Which of the following interprets the slope in the context of the problem?

a. As of 1990, average annual income was $23,286. b. In the ten-year period from 1990–1999, average annual income increased by a total of $1,054. c. Each year in the decade of the 1990s, average annual income increased by $1,054. d. Average annual income rose to a level of $23,286 by the end of 1999.

When temperature is 0 degrees Celsius, the Fahrenheit temperature is 32. When the Celsius temperature is 100, the corresponding Fahrenheit temperature is 212. Express the Fahrenheit temperature as a linear function of $C,$ the Celsius temperature, $F(C).$

a. Find the rate of change of Fahrenheit temperature for each unit change temperature of Celsius. b. Find and interpret $F(28).$ c. Find and interpret $F(-40).$

If the graphs of two linear functions are parallel, describe the relationship between the slopes and the y-intercepts.

If the graphs of two linear functions are perpendicular, describe the relationship between the slopes and the y-intercepts.

If a horizontal line has the equation $f(x)=a$ and a vertical line has the equation $x=a,$ what is the point of intersection? Explain why what you found is the point of intersection.

Explain how to find a line parallel to a linear function that passes through a given point.

Explain how to find a line perpendicular to a linear function that passes through a given point.

For the following exercises, determine whether the lines given by the equations below are parallel, perpendicular, or neither parallel nor perpendicular:

$\begin{array}{c}4x-7y=10 \\ 7x+4y=1\end{array}$

For the following exercises, determine whether the lines given by the equations below are parallel, perpendicular, or neither parallel nor perpendicular:

$\begin{array}{c}3y+x=12 \\ -y=8x+1\end{array}$

For the following exercises, determine whether the lines given by the equations below are parallel, perpendicular, or neither parallel nor perpendicular:

$\begin{array}{c}3y+4x=12 \\ -6y=8x+1\end{array}$

For the following exercises, determine whether the lines given by the equations below are parallel, perpendicular, or neither parallel nor perpendicular:

$\begin{array}{c}6x-9y=10 \\ 3x+2y=1\end{array}$

For the following exercises, determine whether the lines given by the equations below are parallel, perpendicular, or neither parallel nor perpendicular:

$\begin{array}{c}y=\frac{2}{3}x+1 \\ 3x+2y=1\end{array}$

For the following exercises, determine whether the lines given by the equations below are parallel, perpendicular, or neither parallel nor perpendicular:

$\begin{array}{c}y=\frac{3}{4}x+1 \\ -3x+4y=1\end{array}$

For the following exercises, find the x- and *y-*intercepts of each equation

$f(x)=-x+2$

For the following exercises, find the x- and *y-*intercepts of each equation

$g(x)=2x+4$

For the following exercises, find the x- and *y-*intercepts of each equation

$h(x)=3x-5$

For the following exercises, find the x- and *y-*intercepts of each equation

$k(x)=-5x+1$

For the following exercises, find the x- and *y-*intercepts of each equation

$-2x+5y=20$