4.1 Linear functions  (Page 16/27)

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

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

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

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

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

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

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

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

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

An x -intercept $(\mathrm{–2},\text{0})$ 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 $(\mathrm{–6},\text{–2})$ and $(6,\text{–6})$

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

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

$f\left(x\right)=\mathrm{-3}x+2$

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

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

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

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

$x=3$

$x=\mathrm{-2}$

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

If $f$ is a linear function, $f(0.1)=11.5, \text{and} f(0.4)=\mathrm{–5.9},$ find an equation for the function.

Graph the function $f$ on a domain of $[\mathrm{–10},10]:f(x)=0.02x-\mathrm{0.01.}$ Enter the function in a graphing utility. For the viewing window, set the minimum value of $x$ to be $\mathrm{-10}$ and the maximum value of $x$ to be $10.$

Graph the function $f$ on a domain of $[\mathrm{–10},10]:fx)=2,500x+4,000$

[link] shows the input, $w,$ and output, $k,$ for a linear function $k.$ a. Fill in the missing values of the table. b. Write the linear function $k,$ round to 3 decimal places.

[link] shows the input, $p,$ and output, $q,$ for a linear function $q.$ a. Fill in the missing values of the table. b. Write the linear function $k.$

Graph the linear function $f$ on a domain of $\left[-10,10\right]$ for the function whose slope is $\frac{1}{8}$ and y -intercept is $\frac{31}{16}.$ Label the points for the input values of $\mathrm{-10}$ and $10.$

Graph the linear function $f$ on a domain of $\left[-0.1,0.1\right]$ for the function whose slope is 75 and y -intercept is $\mathrm{-22.5.}$ Label the points for the input values of $\mathrm{-0.1}$ and $\mathrm{0.1.}$

Graph the linear function $f$ where $f\left(x\right)=ax+b$ on the same set of axes on a domain of $\left[-4,4\right]$ for the following values of $a$ and $b.$

1. $a=2;b=3$
2. $a=2;b=4$
3. $a=2;b=\mathrm{–4}$
4. $a=2;b=\mathrm{–5}$

Find the value of $x$ if a linear function goes through the following points and has the following slope: $(x,2),(\mathrm{-4},6),m=3$

Find the value of y if a linear function goes through the following points and has the following slope: $(10,y),(25,100),m=\mathrm{-5}$