함수 전체 문제

Does (the referenced table) represent a linear function? If so, find a linear equation that models the data.

Does (the referenced table) represent a linear function? If so, find a linear equation that models the data.

At 6 am, an online company has sold 120 items that day. If the company sells an average of 30 items per hour for the remainder of the day, write an expression to represent the number of items that were sold $n$ after 6 am.

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

$\begin{array}{c}\begin{array}{c} \\ y=\frac{3}{4}x-9\end{array} \\ -4x-3y=8\end{array}$

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

$\begin{array}{c}\begin{array}{c} \\ -2x+y=3\end{array} \\ 3x+\frac{3}{2}y=5\end{array}$

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

Find the x- and y-intercepts of the equation $2x\,+\,7y=-14.$

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

Given below are descriptions of two lines. Find the slopes of Line 1 and Line 2. Is the pair of lines parallel, perpendicular, or neither?

Line 1: Passes through $(-2,-6)$ and $(3,14)$

Line 2: Passes through $(2,6)$ and $(4,14)$

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

Write an equation for a line perpendicular to $f(x)=4x+3$ and passing through the point $(8,10).$

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

Sketch a line with a y-intercept of $(0,5)$ and slope $-\frac{5}{2}$.

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

Graph of the linear function $f(x)=-x+6$.

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

For the two linear functions, find the point of intersection: $\begin{array}{c}x=y+2 \\ 2x-3y=-1\end{array}$

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

A car rental company offers two plans for renting a car.

• Plan A: $25 per day and $0.10 per mile
• Plan B: $40 per day with free unlimited mileage

How many miles would you need to drive for plan B to save you money?

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

Find the area of a triangle bounded by the y axis, the line $f(x)=12-4x$, and the line perpendicular to $f$ that passes through the origin.

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

A town’s population increases at a constant rate. In 2010 the population was 65,000. By 2012 the population had increased to 90,000. Assuming this trend continues, predict the population in 2018.

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

The number of people afflicted with the common cold in the winter months dropped steadily by 25 each year since 2002 until 2012. In 2002, 8,040 people were inflicted. Find the linear function that models the number of people afflicted with the common cold $C$ as a function of the year, $t.$ When will less than 6,000 people be afflicted?

For the following exercises, use the graph in (the referenced figure), showing the profit, $y$, in thousands of dollars, of a company in a given year, $x$, where $x$ represents years since 1980.

Find the linear function $y$, where $y$ depends on $x$, the number of years since 1980.

For the following exercises, use the graph in (the referenced figure), showing the profit, $y$, in thousands of dollars, of a company in a given year, $x$, where $x$ represents years since 1980.

Find and interpret the y-intercept.

For the following exercises, use the graph in (the referenced figure), showing the profit, $y$, in thousands of dollars, of a company in a given year, $x$, where $x$ represents years since 1980.

In 2004, a school population was 1250. By 2012 the population had dropped to 875. Assume the population is changing linearly.

• ⓐ How much did the population drop between the year 2004 and 2012?
• ⓑ What is the average population decline per year?
• ⓒ Find an equation for the population, P, of the school t years after 2004.

For the following exercises, use the graph in (the referenced figure), showing the profit, $y$, in thousands of dollars, of a company in a given year, $x$, where $x$ represents years since 1980.

Draw a scatter plot for the data provided in (the referenced table). Then determine whether the data appears to be linearly related.

For the following exercises, use the graph in (the referenced figure), showing the profit, $y$, in thousands of dollars, of a company in a given year, $x$, where $x$ represents years since 1980.

Draw a best-fit line for the plotted data.