일차함수와 그래프

When hired at a new job selling electronics, you are given two pay options:

• Option A: Base salary of $10,000 a year with a commission of 9% of your sales
• Option B: Base salary of $20,000 a year with a commission of 4% of your sales

How much electronics would you need to sell for option A to produce a larger income?

Determine whether the algebraic equation is linear. $2x+3y=7$

Determine whether the algebraic equation is linear. $6{x}^{2}-y=5$

Determine whether the function is increasing or decreasing.

$f(x)=7x-2$

Determine whether the function is increasing or decreasing.

$g(x)=-x+2$

Given each set of information, find a linear equation that satisfies the given conditions, if possible.

Passes through $(7,5)$ and $(3,17)$

Given each set of information, find a linear equation that satisfies the given conditions, if possible.

x-intercept at $(6,0)$ and y-intercept at $(0,10)$

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

$\begin{array}{c}2x-6y=12 \\ -x+3y=1\end{array}$

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

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

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

$7x+9y=-63$

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

$f(x)=2x-1$

For the following exercises, use the descriptions of the pairs of lines to find the slopes of Line 1 and Line 2. Is each pair of lines parallel, perpendicular, or neither?

• Line 1: Passes through $(5,11)$ and $(10,1)$
• Line 2: Passes through $(-1,3)$ and $(-5,11)$

For the following exercises, use the descriptions of the pairs of lines to find the slopes of Line 1 and Line 2. Is each pair of lines parallel, perpendicular, or neither?

• Line 1: Passes through $(8,-10)$ and $(0,-26)$
• Line 2: Passes through $(2,5)$ and $(4,4)$

For the following exercises, use the descriptions of the pairs of lines to find the slopes of Line 1 and Line 2. Is each pair of lines parallel, perpendicular, or neither?

Write an equation for a line perpendicular to $f(x)=5x-1$ and passing through the point (5, 20).

For the following exercises, use the descriptions of the pairs of lines to find the slopes of Line 1 and Line 2. Is each pair of lines parallel, perpendicular, or neither?

Find the equation of a line with a y- intercept of $(0,\,2)$ and slope $-\frac{1}{2}$.

For the following exercises, use the descriptions of the pairs of lines to find the slopes of Line 1 and Line 2. Is each pair of lines parallel, perpendicular, or neither?

Find the point of intersection for the 2 linear functions: $\begin{array}{c}x=y+6 \\ 2x-y=13\end{array}$

For the following exercises, use the descriptions of the pairs of lines to find the slopes of Line 1 and Line 2. Is each pair of lines parallel, perpendicular, or neither?

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

• Plan A: 25 dollars per day and 10 cents per mile
• Plan B: 50 dollars per day with free unlimited mileage

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

The number of people afflicted with the common cold in the winter months dropped steadily by 50 each year since 2004 until 2010. In 2004, 875 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 no one be afflicted?