19.
Option (B) is the correct one.
Explanation:
The equation of line be is ,
y = 2x-4,
we have general equation give by,
y = mx +c
wherr m is the slope of the line and x and y are the coordinates changing,
Comparing these two we get the slop of line B as 2.
A thing you need to know here that product of slopes of a line perpendicular to another is -1.
Using this relation,
The slope of line a will be -1/2.
Let A pass through a coordinate (x,y).
Now,
Slope will be give by,
[tex] \frac{y - 1}{x +2} = - \frac{1}{2} \\ y - 1= - \frac{x}{2} - 1 \\ y = - \frac{x}{2} [/tex]
20.
Option (A) is the correct one.
How?:
Equation of line B is y = 3x-1.
Once again using the general equation for a line,
y =mx+c
Slope of B will be 3.
Now for a pair of parallel lines their slopes are equal.
So,
Slope of A must also be 3.
Applying the generation equation for a line on A gives,
y = 3x+c
Since A is passing though coordinates (2,4) the values must satisfy this equation,
So we have,
[tex]4 = 2(3) + c \\ c = 4 - 6 = - 2[/tex]
Now that we have value for c.
We can get the the equation we need.
So we have,
y = 3x -2.
Hope it helps.
