2.1 Graphs of linear functions  (Page 10/15)

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

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

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

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

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

$f\left(x\right)=-x+2$

$g\left(x\right)=2x+4$

$h\left(x\right)=3x-5$

$k\left(x\right)=-5x+1$

$-2x+5y=20$

$7x+2y=56$

• Line 1: Passes through $(0,6)$ and $(3,\mathrm{-24})$
• Line 2: Passes through $(\mathrm{-1},19)$ and $(8,\mathrm{-71})$

• Line 1: Passes through $(\mathrm{-8},\mathrm{-55})$ and $(10,89)$
• Line 2: Passes through $(9,\mathrm{-44})$ and $(4,\mathrm{-14})$

• Line 1: Passes through $(2,3)$ and $(4,-1)$
• Line 2: Passes through $(6,3)$ and $(8,5)$

• Line 1: Passes through $(1,7)$ and $(5,5)$
• Line 2: Passes through $(\mathrm{-1},\mathrm{-3})$ and $(1,1)$

• Line 1: Passes through $(0,5)$ and $(3,3)$
• Line 2: Passes through $(1,\mathrm{-5})$ and $(3,\mathrm{-2})$

• Line 1: Passes through $(2,5)$ and $(5,\mathrm{-1})$
• Line 2: Passes through $(\mathrm{-3},7)$ and $(3,\mathrm{-5})$

Write an equation for a line parallel to $f\left(x\right)=-5x-3$ and passing through the point $(2,\text{ –}12).$

Write an equation for a line parallel to $g(x)=3x-1$ and passing through the point $(4,9).$

Write an equation for a line perpendicular to $h(t)=-2t+4$ and passing through the point $(\text{-}4,\text{ –}1).$

Write an equation for a line perpendicular to $p(t)=3t+4$ and passing through the point $(3,1).$

Find the point at which the line $f(x)=-2x-1$ intersects the line $g(x)=-x.$

Find the point at which the line $f(x)=2x+5$ intersects the line $g(x)=-3x-5.$

Use algebra to find the point at which the line $f\left(x\right)= -\frac{4}{5}x +\frac{274}{25}$ intersects the line $h\left(x\right)=\frac{9}{4}x+\frac{73}{10}.$

Use algebra to find the point at which the line $f\left(x\right)=\frac{7}{4}x+\frac{457}{60}$ intersects the line $g\left(x\right)=\frac{4}{3}x+\frac{31}{5}.$

$f\left(x\right)=-x-1$

$f\left(x\right)=-2x-1$

$f\left(x\right)=-\frac{1}{2}x-1$

$f\left(x\right)=2$

$f\left(x\right)=2+x$

$f\left(x\right)=3x+2$

An x -intercept of $(–\text{4},\text{ 0})$ and y -intercept of $(0,\text{ –2})$

An x -intercept of $(–\text{2},\text{ 0})$ and y -intercept of $(0,\text{ 4})$

A y -intercept of $(0,\text{ 7})$ and slope $-\frac{3}{2}$

A y -intercept of $(0,\text{ 3})$ and slope $\frac{2}{5}$

Passing through the points $(–\text{6},\text{ –2})$ and $(\text{6},\text{ –6})$

Passing through the points $(–\text{3},\text{ –4})$ and $(\text{3},\text{ 0})$

$f\left(x\right)=-2x-1$

$g\left(x\right)=-3x+2$

$h\left(x\right)=\frac{1}{3}x+2$

$k\left(x\right)=\frac{2}{3}x-3$

$f\left(t\right)=3+2t$

$p\left(t\right)=-2+3t$

$x=3$

$x=-2$

$r\left(x\right)=4$

$q\left(x\right)=3$

$4x=-9y+36$

$\frac{x}{3}-\frac{y}{4}=1$

$3x-5y=15$

$3x=15$

$3y=12$

If $g(x)$ is the transformation of $f(x)=x$ after a vertical compression by $\frac{3}{4},$ a shift right by 2, and a shift down by 4

1. Write an equation for $g\left(x\right).$
2. What is the slope of this line?
3. Find the y- intercept of this line.

If $g(x)$ is the transformation of $f(x)=x$ after a vertical compression by $\frac{1}{3},$ a shift left by 1, and a shift up by 3

1. Write an equation for $g\left(x\right).$
2. What is the slope of this line?
3. Find the y- intercept of this line.

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

$\begin{array}{c}2x-3y=12\\ 5y+x=30\end{array}$

$\begin{array}{c}2x=y-3\\ y+4x=15\end{array}$

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

$\begin{array}{c}5x+3y=-65\\ x-y=-5\end{array}$

Find the equation of the line parallel to the line $g\left(x\right)=-0.\text{01}x\text{+}\text{2}\text{.01}$ through the point $(\text{1},\text{ 2}).$

Find the equation of the line perpendicular to the line $g\left(x\right)=-0.\text{01}x\text{+2}\text{.01}$ through the point $(\text{1},\text{ 2}).$

Find the point of intersection of the lines $f$ and $g.$

Where is $f\left(x\right)$ greater than $g\left(x\right)?$ Where is $g\left(x\right)$ greater than $f\left(x\right)?$

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

• Plan A: $30 per day and $0.18 per mile
• Plan B: $50 per day with free unlimited mileage

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

A cell phone company offers two plans for minutes.

• Plan A: $20 per month and $1 for every one hundred texts.
• Plan B: $50 per month with free unlimited texts.

How many texts would you need to send per month for plan B to save you money?

A cell phone company offers two plans for minutes.

• Plan A: $15 per month and $2 for every 300 texts.
• Plan B: $25 per month and $0.50 for every 100 texts.

How many texts would you need to send per month for plan B to save you money?