Recall that the slope intercept of a line equation is
y = mx+b
where m is the slope and b is the y-intercept. Given the line equations, we should operate both sides of it, so we end up having the y term on one side on its own.
First, we start with the equation
[tex]\text{ -}\frac{1}{2}x+y=4[/tex]By adding (1/2)x on both sides, we get
[tex]y=\frac{1}{2}x+4[/tex]which is the slope-intercept form of this line equation.
On the other side, we have the equation
[tex]2x\text{ -3y=8}[/tex]First, we start by adding 3y on both sides, so we get
[tex]2x\text{ = 8+3y}[/tex]Then, we subtract 8 on both sides, so we have
[tex]3y\text{ = 2x-8}[/tex]Finally, we divide both sides by 3, so we get
[tex]y=\frac{2x\text{ -8}}{3}=\frac{2}{3}x\text{ -}\frac{8}{3}[/tex]which is the slope intercept form of the second line equation.
