<< Chapter < Page | Chapter >> Page > |
$\begin{array}{c}3y+x=12\\ -y=8x+1\end{array}$
neither parallel or perpendicular
$\begin{array}{c}3y+4x=12\\ -6y=8x+1\end{array}$
$\begin{array}{c}6x-9y=10\\ 3x+2y=1\end{array}$
perpendicular
$\begin{array}{c}y=\frac{2}{3}x+1\\ 3x+2y=1\end{array}$
$\begin{array}{c}y=\frac{3}{4}x+1\\ -3x+4y=1\end{array}$
parallel
For the following exercises, find the x - and y- intercepts of each equation
$f\left(x\right)=-x+2$
$g\left(x\right)=2x+4$
$(\u20132\text{,}0)$ ; $(0\text{,4})$
$h\left(x\right)=3x-5$
$k\left(x\right)=-5x+1$
$(\frac{1}{5}\text{,}0)$ ; $(0\text{,1})$
$-2x+5y=20$
For the following exercises, use the descriptions of each pair of lines given below to find the slopes of Line 1 and Line 2. Is each pair of lines parallel, perpendicular, or neither?
$\text{Line1}:\text{\hspace{0.17em}}m=8\text{Line2}:\text{\hspace{0.17em}}m=\u20136\text{Neither}$
$\text{Line1}:\text{\hspace{0.17em}}m=\u2013\frac{1}{2}\text{Line2}:\text{\hspace{0.17em}}m=2\text{Perpendicular}$
$\text{Line1}:\text{\hspace{0.17em}}m=\u20132\text{Line2}:\text{\hspace{0.17em}}m=\u20132\text{Parallel}$
Write an equation for a line parallel to $f\left(x\right)=-5x-3$ and passing through the point $(2,\text{\u2013}12).$
Write an equation for a line parallel to $g(x)=3x-1$ and passing through the point $(4,9).$
$g(x)=3x-3$
Write an equation for a line perpendicular to $h(t)=-2t+4$ and passing through the point $(\text{-}4,\text{\u2013}1).$
Write an equation for a line perpendicular to $p(t)=3t+4$ and passing through the point $(3,1).$
$p(t)=-\frac{1}{3}t+2$
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 $g(x)=-3x-5.$
$\left(-2,1\right)$
Use algebra to find the point at which the line $f\left(x\right)=-\frac{4}{5}x+\frac{274}{25}$ intersects the line $h\left(x\right)=\frac{9}{4}x\text{\hspace{0.17em}}\text{\hspace{0.17em}}+\text{\hspace{0.17em}}\text{\hspace{0.17em}}\frac{73}{10}.$
Use algebra to find the point at which the line $f\left(x\right)=\frac{7}{4}x\text{\hspace{0.17em}}\text{\hspace{0.17em}}+\text{\hspace{0.17em}}\text{\hspace{0.17em}}\frac{457}{60}$ intersects the line $g\left(x\right)=\frac{4}{3}x\text{\hspace{0.17em}}\text{\hspace{0.17em}}+\text{\hspace{0.17em}}\text{\hspace{0.17em}}\frac{31}{5}.$
$\left(-\frac{17}{5},\frac{5}{3}\right)$
For the following exercises, the given linear equation with its graph in [link] .
$f\left(x\right)=-x-1$
$f\left(x\right)=-\frac{1}{2}x-1$
$f\left(x\right)=2+x$
For the following exercises, sketch a line with the given features.
An x -intercept of $(\u2013\text{4},\text{0})$ and y -intercept of $(0,\text{\u20132})$
An x -intercept of $(\u2013\text{2},\text{0})$ and y -intercept of $(0,\text{4})$
A y -intercept of $(0,\text{7})$ and slope $-\frac{3}{2}$
Passing through the points $(\u2013\text{6},\text{\u20132})$ and $(\text{6},\text{\u20136})$
Passing through the points $(\u2013\text{3},\text{\u20134})$ and $(\text{3},\text{0})$
For the following exercises, sketch the graph of each equation.
$f\left(x\right)=-2x-1$
$h\left(x\right)=\frac{1}{3}x+2$
$f\left(t\right)=3+2t$
$p\left(t\right)=-2\text{\hspace{0.17em}}+\text{\hspace{0.17em}}3t$
$r\left(x\right)=4$
$4x=-9y+36$
$3x-5y=15$
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
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
For the following exercises,, write the equation of the line shown in the graph.
For the following exercises, find the point of intersection of each pair of lines if it exists. If it does not exist, indicate that there is no point of intersection.
$\begin{array}{c}y=\frac{3}{4}x+1\\ -3x+4y=12\end{array}$
no point of intersection
$\begin{array}{c}2x-3y=12\\ 5y+x=30\end{array}$
$\begin{array}{c}2x=y-3\\ y+4x=15\end{array}$
$(\text{2},\text{7})$
$\begin{array}{c}x-2y+2=3\\ x-y=3\end{array}$
$\begin{array}{c}5x+3y=-65\\ x-y=-5\end{array}$
$(\u201310,\text{\u20135})$
Find the equation of the line parallel to the line $g\left(x\right)=-0.\text{01}x\text{\hspace{0.17em}}\text{+}\text{\hspace{0.17em}}\text{2}\text{.01}$ 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 $(\text{1},\text{2}).$
$y=100x-98$
For the following exercises, use the functions $f\left(x\right)=-0.\text{1}x\text{+200and}g\left(x\right)=20x+\mathrm{0.1.}$
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 $f\left(x\right)?$
$x<\frac{1999}{201}x>\frac{1999}{201}$
A car rental company offers two plans for renting a car.
How many miles would you need to drive for plan B to save you money?
A cell phone company offers two plans for minutes.
How many texts would you need to send per month for plan B to save you money?
Less than 3000 texts
A cell phone company offers two plans for minutes.
How many texts would you need to send per month for plan B to save you money?
Notification Switch
Would you like to follow the 'Precalculus' conversation and receive update notifications?