Question

tenzing property for each family of lines. (a) 5x + y = C (g) Ax + By = 0 (i) y = x tan 50° + b 2. Write the equation for the family of lines with the following characterizin (a) parallel to x + y = 10 List til 1. (c) Ax - 7y=21 (e) y = mx + 5 (b) 6x + By = 24 (d) y = 4x + b (1) kx + kyk (h) m(x + 2)=y-1 (i) x=aLetter a and b

Answer 1

(a) y = -x + b

(b) y = (2/3)x + b

Step-by-step 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:

`\begin{gathered} (-3)/(2)* m=-1 \\ 2*(-3)/(2)* m=2*(-1) \\ -3* m=-2 \\ (-3* m)/(-3)=(-2)/(-3) \\ m=(2)/(3) \end{gathered}`

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 =