Answer:
(a) y = -x + b
(b) y = (2/3)x + b
Explanation:
a.
Two lines are parallel if they have the same slope. So, to find the family of equations, we need to identify the slope of x + y = 10
In an equation with the form y = mx + b, m is the slope.
So, to know the slope we need to solve the equation x + y = 10 for y as:
x + y = 10
x + y - x = 10 - x
y = 10 - x
y = - x + 10
Therefore, the slope of the line is -1, and the family of lines that are parallel will also o havaan slope equal to . It means that the equation is:
y =-- x + b
Where b can be any value.
b.
On the other hand, two lines are perpendicular if the multiplication of their slopes is equal to -1.
So, the slope of 3x + 2y = 7 is:
3x + 2y = 7
3x + 2y - 3x = 7 - 3x
2y = 7 - 3x
2y/2 = 7/2 - (3/2)x
y = (-3/2)x + 7/2
Now, a slope of a line that is perpendicular to -3/2 is:
[tex]\begin{gathered} \frac{-3}{2}\times m=-1 \\ 2\times\frac{-3}{2}\times m=2\times(-1) \\ -3\times m=-2 \\ \frac{-3\times m}{-3}=\frac{-2}{-3} \\ m=\frac{2}{3} \end{gathered}[/tex]Therefore, the equation of the family of lines is:
y = (2/3)x + b
2y = 7 - 3x
2On th other the
1. It means that the equation is:
y =
