The slope-intercept form is y = mx + b while the standard form is Ax + By = C
To convert a slope-intercept form to standard form, say,
4y - 12 = 3x
First, we need to transform it to a y=mx+b form. That is,
[tex]\: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: \: \: \: \: \ 4y - 12 = 3x \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: \: \: \: \: \ \: \: \: \:\: \: \: \: \: \: \: \: \: \: \ \ 4y = 3x + 12 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: \: \: \: \:\: \: \: \: \: \: \: \: \: \: \ \: \ \: y = \frac{3}{4} x + \frac{12}{4}\\\purple{\boxed{Slope-Int.\:form}}\: \: y = \frac{3}{4} x +3\: [/tex]
Then, to convert it to standard form, we have,
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: y = \frac{3}{4} x + 3 \\ -\frac{3}{4}x +y= 3 [/tex]
Lastly, multiplying both sides with 4, we get,
[tex]\: \: \: \:\: \: \: \: \: \:-3x+4y=12\: \red{\boxed{Standard\:Form}}[/tex]
