## Intermediate Algebra (12th Edition)

$\text{Slope-Intercept Form: } y=4x \\\text{Standard Form: } 4x-y=0$
Use the Two-Point Form of linear equations to find the equation of the line passing through $( 0,0 )$ and $( 1,4 ).$ Using $y-y_1=\dfrac{y_1-y_2}{x_1-x_2}(x-x_1)$ or the Two-Point Form of linear equations, the equation of the line with the given conditions is \begin{array}{l}\require{cancel} y-0=\dfrac{0-4}{0-1}(x-0) \\\\ y=\dfrac{-4}{-1}x \\\\ y=4x .\end{array} Using $y=mx+b$ or the Slope-Intercept Form of linear equations, the equation above is equivalent to \begin{array}{l}\require{cancel} y=4x+0 \\\\ y=4x .\end{array} Using $Ax+By=C$ or the Standard Form of linear equations, the equation above is equivalent to \begin{array}{l}\require{cancel} -4x+y=0 \\\\ 4x-y=0 .\end{array} Hence, the equation of the line is \begin{array}{l}\require{cancel} \text{Slope-Intercept Form: } y=4x \\\text{Standard Form: } 4x-y=0 .\end{array}