Respuesta :
To answer this question, we have to use the concept of a slope of a line. The slope of a line is given by the next formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Now, we have that the two points are (a, -1) and (4, -4), and we can label them as follows:
• (a, -1) ---> x1 = a, y1 = -1
,• (4, -4) ---> x2 = 4, y2 = -4
We already know that m = 3. Then we have:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ 3=\frac{-4-(-1)}{4-a} \\ 3=\frac{-4+1}{4-a} \\ 3=\frac{-3}{4-a} \end{gathered}[/tex]Now, if we multiply both sides of the equation by (4 - a), we have:
[tex]\begin{gathered} (4-a)\cdot3=(4-a)\cdot\frac{-3}{(4-a)} \\ (4-a)\cdot3=\frac{(4-a)}{(4-a)}\cdot(-3)\Rightarrow\frac{(4-a)}{(4-a)}=1 \\ (4-a)\cdot3=-3 \end{gathered}[/tex]We need to apply here the distributive property. Then we have:
[tex]\begin{gathered} 4\cdot3+(-a)(3)=-3 \\ 12-3a=-3 \end{gathered}[/tex]Now, we have to subtract 12 from both sides of the equation, and then we need to divide the result by -3 as follows:
[tex]\begin{gathered} 12-12-3a=-3-12 \\ -3a=-15 \\ \frac{-3a}{-3}=\frac{-15}{-3} \\ a=5 \end{gathered}[/tex]We can check this result if we substitute the result into the original equation as follows:
x1 = 5, y1 = -1
x2 = 4, y2 = -4
[tex]\begin{gathered} 3=\frac{-4-(-1)}{4-5}_{} \\ 3=\frac{-4+1}{-1} \\ 3=\frac{-3}{-1} \\ 3=3\Rightarrow This\text{ is True.} \end{gathered}[/tex]In summary, therefore, the value for a is equal to 5, a = 5.
