Given the point-slope equation
[tex]y+1=\frac{2}{3}(x-8)[/tex]
Simplify as shown below
[tex]\begin{gathered} y+1=\frac{2}{3}x-8\cdot\frac{2}{3}=\frac{2}{3}x-\frac{16}{3} \\ \Rightarrow-\frac{2}{3}x+y=-\frac{16}{3}-1=-\frac{19}{3} \\ \Rightarrow-\frac{2}{3}x+y=-\frac{19}{3} \end{gathered}[/tex]
The answer is -2x/3+y=-19/3. Write -2/3 in the first gap, 1 in the second gap, and -19/3 in the third one.
How to multiply fractions
[tex]\begin{gathered} \frac{a}{b}\cdot\frac{c}{d}=\frac{a\cdot c}{b\cdot d} \\ \Rightarrow8\cdot\frac{2}{3}=\frac{8}{1}\cdot\frac{2}{3}=\frac{8\cdot2}{1\cdot3}=\frac{16}{3} \end{gathered}[/tex]
How to add fractions,
[tex]\begin{gathered} \frac{a}{b}+\frac{c}{d}=\frac{\text{ad+cd}}{bd} \\ \Rightarrow-\frac{16}{3}-1=-\frac{16}{3}-\frac{3}{3}=\frac{-16\cdot3-3\cdot3}{3\cdot3}=\frac{-48-9}{9}=-\frac{57}{9}=-\frac{19}{3} \end{gathered}[/tex]
