[math]m=\frac{3-\left(-3\right)}{8-\left(-2\right)}=\frac{6}{10}=\frac{3}{5}[/math]

[math]y-3=\frac{3}{5}\left(x-8\right)[/math]

Solve for y from the point-slope form:[math]y-3=\frac{3}{5}\left(x-8\right)[/math][br]Distribute: [math]y-3=\frac{3}{5}x-\frac{24}{5}[/math][br]Add 3 to both sides: [math]y-3\left(+3\right)=\frac{3}{5}x-\frac{24}{5}\left(+3\right)[/math] make 3 have the same denominator as -24/5 so you are adding 15/5 [math]y-3\left(+3\right)=\frac{3}{5}x-\frac{24}{5}\left(+\frac{15}{5}\right)[/math][br]Simplify: [math]y=\frac{3}{5}x-\frac{9}{5}[/math]

You want to get x and y terms on the left side of the equation from the point-slope form:[math]y-3=\frac{3}{5}\left(x-8\right)[/math][br]Get whole numbers so multiply by the denominators [math]5\cdot\left(y-3\right)=\frac{3}{5}\left(x-8\right)\cdot5[/math] resulting in [math]5y-15=3\left(x-8\right)[/math][br]Distribute: [math]5y-15=3x-24[/math] [br]Move 3x to the left side by subtracting 3x from both sides [math]5y-15-3x=3x-24-3x[/math] resulting in [math]-3x+5y-15=-24[/math][br]Move -15 to the right side by adding 15 to both sides [math]-3x+5y-15+15=-24+15[/math] resulting in [math]-3x+5y=-9[/math][br]The x term cannot be negative so multiply the entire equation by -1. [math]-1\left(-3x+5y=-9\right)[/math][br]Resulting in: [math]3x-5y=9[/math]