- Point-Slope form: [tex] y-y_1=m(x-x_1) [/tex] , with [tex] (x_1,y_1) [/tex] as a point on the line and m = slope
- Slope-Intercept form: [tex] y=mx+b [/tex] , with m = slope and b = y-intercept.
- Slope Formula: [tex] \frac{y_2-y_1}{x_2-x_1} [/tex]
So firstly, we have to convert this standard form equation into slope-intercept form. To start with, add x on both sides of the equation: [tex] 3y=x+6 [/tex]
Next, divide both sides by 3 and your slope-intercept form is [tex] y=\frac{1}{3}x+2 [/tex] .
Next, since we know one of the points, the y-intercept (0,2), and the slope, 1/3. We can use the slope formula to get to point-slope form. Our equation looks like this:
[tex] \frac{y-2}{x-0}=\frac{1}{3}\\\\\frac{y-2}{x}=\frac{1}{3} [/tex]
For this, just multiply both sides by x and your point-slope form is [tex] y-2=\frac{1}{3}(x) [/tex]
