Respuesta :
Answer:
1. The slope of the line is [tex]m=\frac{-2b+3}{2a}[/tex].
2. The value of a is 18.
Step-by-step explanation:
If a line passes through two points, then the slope of the line is
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
(1)
It is given that the line passes through the points (-a + 3, b - 3) and (a + 3, -b). So, the slope of the line is
[tex]m=\frac{-b-(b-3)}{a+3-(-a+3)}[/tex]
[tex]m=\frac{-b-b+3}{a+3+a-3)}[/tex]
[tex]m=\frac{-2b+3}{2a}[/tex]
The slope of the line is [tex]m=\frac{-2b+3}{2a}[/tex].
(2)
If the line passing through the points (a, 1) and (6, 5), then the slope of the line is
[tex]m_1=\frac{5-1}{6-a}=\frac{4}{6-a}[/tex]
If the line passing through the points (2, 7) and (a + 2, 1), then the slope of the line is
[tex]m_2=\frac{1-7}{a+2-2}=\frac{-6}{a}[/tex]
The slopes of two parallel lines are same.
[tex]m_1=m_2[/tex]
[tex]\frac{4}{6-a}=\frac{-6}{a}[/tex]
On cross multiplication we get
[tex]4a=-6(6-a)[/tex]
[tex]4a=-36+6a[/tex]
[tex]4a-6a=-36[/tex]
[tex]-2a=-36[/tex]
Divide both sides by -2.
[tex]a=18[/tex]
Therefore the value of a is 18.
