The general form for a line is
![\[ax+by=c\]](https://tentotwelvemath.com/wp-content/ql-cache/quicklatex.com-7bffaa0dde3e03fe4367e22917a9a041_l3.png "Rendered by QuickLaTeX.com")
where 
and 
are integers.
Using either the slope intercept form (
) or the general form (
) we can calculate all the critical values of a straight line. These are: the 
intercept, the 
intercept and the slope.
Example 1: convert 
to form:
![\begin{align*}3x+2y&=-5 &\text{take $3x$ from both sides} \\[10pt] 2y&=-3x-5&\text{divide all terms by 2}\\[10pt] y&=-\frac{3}{2}x-\frac{5}{2}\end{align*}](https://tentotwelvemath.com/wp-content/ql-cache/quicklatex.com-2d4eabf76a888f5df226013ba54a8883_l3.png "Rendered by QuickLaTeX.com")
Example 2: convert 
to general form:
![\begin{align*} y&=\frac{1}{4}x+3 &\text{multiply every term by 4}\\[10pt] 4y& = x + 12&\text{subtract 12 from both sides}\\[10pt] 4y-12&=x &\text{subtract $4y$ from both sides}\\[10pt] -12&=x-4y\end{align*}](https://tentotwelvemath.com/wp-content/ql-cache/quicklatex.com-260bc78c6da17285a8fa474db0920b3b_l3.png "Rendered by QuickLaTeX.com")
Finding the y intercept
The y intercept is the point where the line cuts the y-axis. The x coordinate is zero. To find the y intercept, we substitute 
for .
Example 3: Find the y intercept of the line
![\begin{align*}3x+2y&=-5 &\text{substitute $x=0$} \\[10pt] 3(0)+2y&=-5&\text{simplify}\\[10pt] 2y&=-5 &\text{divide both sides by 2}\\[10pt] y&=-\frac{5}{2}&\text{$y$ intercept is }-\frac{5}{2}\end{align*}](https://tentotwelvemath.com/wp-content/ql-cache/quicklatex.com-779deec4e414f730e80bf77bd966b2bb_l3.png "Rendered by QuickLaTeX.com")
Finding the x intercept
The x intercept is the point that is on the line and on the x axis. The y coordinate is zero. To find the x intercept, we substitute for .
Example 4: Find the x intercept of the line
![\begin{align*}3x+2y&=-5 &\text{substitute $y=0$} \\[10pt] 3x+2(0)&=-5&\text{simplify}\\[10pt] 3x&=-5 &\text{divide both sides by 3}\\[10pt] x&=-\frac{3}{2}&\text{$x$ intercept is }-\frac{3}{2}\end{align*}](https://tentotwelvemath.com/wp-content/ql-cache/quicklatex.com-42adcc5b15554c97e2f10992d59b334e_l3.png "Rendered by QuickLaTeX.com")
Calculations
Example: Video (3:31 mins)
Examples x y intercepts slope general form
Calculate the x and y intercepts and the slope. Rewrite the equation in the alternate form. Use fractions or terminating decimals, don’t round decimals.