2." Find the equation of the line through the intersection of lines x + 2y - 3 = 0 and
4x - y + 7 = 0 and which is parallel to 5x + 4y – 20 = 0
(Ans. 15x + 12y - 7 = 0)

Step-by-step explanation:

hello :

1 )  calculate  point the intersection of lines lines ;

x + 2y - 3 = 0 ...(*)

4x - y + 7 = 0...(**)

solve this system : multiply (**) by 2

x+2y-3 = 0 (*)

8x-2y +14 = 0 ..(***)

add (*) and (***) : 9x+11 =0

9x = -11   so : x = -11/9  put this value in (**):

4(-11/9) - y + 7 = 0

y = 7-44/9 = 19/9

the point is A(-11/9  ; 19/9)

2) my line is parallel to 5x + 4y – 20 = 0

so : same slope now calculate the slope of the line :5x + 4y – 20 = 0

4y = -5x+20

y = -5/4 x + 5   the slope is : -5/4

an equation is : y - 19/9 = -5/4(x+11/9)

y -19/9 = -5/4 x - 55/36

multiply by 36 : 36y-76 = -45 x -55

36y +45x -21 =0   divid by 3 :

12y+15x -7 =0

conclusionn : 15x+12y -7 =0

same (Ans. 15x + 12y - 7 = 0) thanks

options a,b,c are the right answer.

step-by-step explanation:

a linear parent function is always represented as y = x

if we write this function in the form of y=mx+c

⇒

or  

now if we plot a graph we will find these characteristics:

1) y intercept of the graph is zero so its a straight line passing through origin.

2) as we can see in both the forms of function written, values of x and y may be either positive or negative for the positive slope means points on the graph are either in first quadrant or in third one.

3) it's slope is one.

d. you cannot tell because there are no values shown.