Exercises: Drawing graphs of linear functions

$\mathrm{f}(\mathrm{x})=2\mathrm{x}-5$

First read off the $y$-axis intercept and the slope from the function equation.

$\Rightarrow {\mathrm{P}}_{\mathrm{y}}\left(0|-5\right)$

$\Rightarrow m_f=2$

Calculate the point of intersection with the $x$-axis. Set the function term equal to 0.

$\Rightarrow {\mathrm{P}}_{\mathrm{x}}\left(2.5|0\right)$

$\mathrm{f}(\mathrm{x})=-\mathrm{x}-3$

First read off the $y$-axis intercept and the slope from the function equation.

$\Rightarrow {\mathrm{P}}_{\mathrm{y}}\left(0|-3\right)$

$\Rightarrow m_f=-1$

$\Rightarrow {\mathrm{P}}_{\mathrm{x}}(-3|0)$

$\mathrm{f}(\mathrm{x})=\frac{1}{2}\mathrm{x}+1$

First read off the $y$-axis intercept and the slope from the function equation.

$\Rightarrow {\mathrm{P}}_{\mathrm{y}}\left(0|1\right)$

$\Rightarrow m_f=\frac{1}{2}$

Calculate the point of intersection with the $x$-axis. Set the function term equal to 0.

$\Rightarrow {\mathrm{P}}_{\mathrm{x}}(-2|0)$

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

First read off the $y$-axis intercept and the slope from the function equation.

$\Rightarrow {\mathrm{P}}_{\mathrm{y}}\left(0|-2\right)$

$\Rightarrow m_f=-\frac{1}{2}$

Calculate the point of intersection with the $x$-axis. Set the function term equal to 0..

$\Rightarrow {\mathrm{P}}_{\mathrm{x}}(-4|0)$

$\mathrm{f}(\mathrm{x})=\frac{1}{3}\mathrm{x}-\frac{1}{2}$

First read off the $y$-axis intercept and the slope from the function equation.

$\Rightarrow {\mathrm{P}}_{\mathrm{y}}\left(0|-\frac{1}{2}\right)$

$\Rightarrow m_f=\frac{1}{3}$

Calculate the point of intersection with the $x$-axis. Set the function term equal to 0.

$\Rightarrow {\mathrm{P}}_{\mathrm{x}}\left(\frac{3}{2}|0\right)$

$\mathrm{f}(\mathrm{x})=-\frac{1}{4}\mathrm{x}+\frac{3}{2}$

First read off the $y$-axis intercept and the slope from the function equation.

$\Rightarrow {\mathrm{P}}_{\mathrm{y}}\left(0|\frac{3}{2}\right)$

$\Rightarrow m_f=-\frac{1}{4}$

Calculate the point of intersection with the $x$-axis. Set the function term equal to 0.

$\Rightarrow {\mathrm{P}}_{\mathrm{x}}\left(6|0\right)$

$\mathrm{f}(\mathrm{x})=\frac{2}{3}\mathrm{x}+2$

First read off the $y$-axis intercept and the slope from the function equation.

$\Rightarrow {\mathrm{P}}_{\mathrm{y}}\left(0|2\right)$

$\Rightarrow m_f=\frac{2}{3}$

Calculate the point of intersection with the $x$-axis. Set the function term equal to 0.

$\Rightarrow {\mathrm{P}}_{\mathrm{x}}(-3|0)$

$\mathrm{f}(\mathrm{x})=-\frac{3}{4}\mathrm{x}-1$

First read off the $y$-axis intercept and the slope from the function equation.

$\Rightarrow {\mathrm{P}}_{\mathrm{y}}\left(0|-1\right)$

$\Rightarrow m_f=-\frac{3}{4}$

Calculate the point of intersection with the $x$-axis. Set the function term equal to 0.

$\Rightarrow {\mathrm{P}}_{\mathrm{x}}(-\frac{4}{3}|0)$

$\mathrm{f}(\mathrm{x})=-3\mathrm{x}+\frac{5}{10}$

First read off the $y$-axis intercept and the slope from the function equation.

$\Rightarrow {\mathrm{P}}_{\mathrm{y}}\left(0|\frac{5}{10}\right)$

$\Rightarrow m_f=-3$

Calculate the point of intersection with the $x$-axis. Set the function term equal to 0.

$\Rightarrow {\mathrm{P}}_{\mathrm{x}}\left(\frac{1}{6}|0\right)$

$\mathrm{f}(\mathrm{x})=\frac{5}{7}\mathrm{x}-\frac{12}{4}=\frac{5}{7}\mathrm{x}-3$

First read off the $y$-axis intercept and the slope from the function equation.

$\Rightarrow {\mathrm{P}}_{\mathrm{y}}\left(0|-3\right)$

$\Rightarrow m_f=\frac{5}{7}$

Calculate the point of intersection with the $x$-axis. Set the function term equal to 0.

$\Rightarrow {\mathrm{P}}_{\mathrm{x}}\left(\frac{21}{5}|0\right)$