4.1 Linear functions  (Page 15/27)

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 $f\left(x\right)=a$ 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.

$y=\frac{1}{4}x+6$

$y=3x-5$

$y=3x^2-2$

$3x+5y=15$

$3x^2+5y=15$

$3x+5y^2=15$

$-2x^2+3y^2=6$

$-\frac{x-3}{5}=2y$

$f\left(x\right)=4x+3$

$g\left(x\right)=5x+6$

$a\left(x\right)=5-2x$

$b\left(x\right)=8-3x$

$h\left(x\right)=\mathrm{-2}x+4$

$k\left(x\right)=\mathrm{-4}x+1$

$j\left(x\right)=\frac{1}{2}x-3$

$p\left(x\right)=\frac{1}{4}x-5$

$n\left(x\right)=-\frac{1}{3}x-2$

$m\left(x\right)=-\frac{3}{8}x+3$

$(2,4)$ and $(4,\text{10})$

$(1,\text{5})$ and $(4,\text{11})$

$(\mathrm{–1},\text{4})$ and $(5,\text{2})$

$(8,\mathrm{–2})$ and $(4,6)$

$(6,11)$ and $(\mathrm{–4},\text{3})$

$f(-5)=\mathrm{-4},$ and $f(5)=2$

$f(\mathrm{-1})=4,$ and $f(5)=1$

Passes through $(2,4)$ and $(4,10)$

Passes through $(1,5)$ and $(4,11)$

Passes through $(\mathrm{-1},\text{4})$ and $(5,\text{2})$

Passes through $(\mathrm{-2},\text{8})$ and $(4,\text{6})$

x intercept at $(\mathrm{-2},\text{0})$ and y intercept at $(0,\mathrm{-3})$

x intercept at $(\mathrm{-5},\text{0})$ and y intercept at $(0,\text{4})$

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

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

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

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

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

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

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

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

$-2x+5y=20$

$7x+2y=56$

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 $(9,-44)$ and $(4,-14)$

Line 1: Passes through $(2,3)$ and $(4,\mathrm{-1})$

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 $(2,5)$ and $(5,-1)$

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 $(4,9).$