Exercises: Finding line equations

Gradient

Determine the gradient $\mathrm{m}$ .

$\mathrm{m}={\displaystyle \frac{△\mathrm{y}}{△\mathrm{x}}}={\displaystyle \frac{{\mathrm{y}}_2-{\mathrm{y}}_1}{{\mathrm{x}}_2-{\mathrm{x}}_1}}$

Insert the two points into the formula for the gradient.

$\mathrm{m}={\displaystyle \frac{3-(-3)}{0-2}}={\displaystyle \frac{6}{-2}}=-3$

Function equation

Determine the function equation.

$\mathrm{y}=\mathrm{m}\cdot \mathrm{x}+\mathrm{t}$

Insert m into the general line equation.

$\mathrm{y}=-3\mathrm{x}+\mathrm{t}$

Insert one of the two points into the function equation.

$3=-3\cdot 0+\mathrm{t}$

$\mathrm{t}=3$

Substitute t into the function equation.

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