two math equation

1.
2x - 5y + 10 = 0
Slope = -(coefficient of x)/(coefficient of y) = -2/(-5) = 2/5

Put y = 0,
2x - 5(0) + 10 = 0
2x + 10 = 0
x = -5
So the x-intercept is -5


2.
Slope of A = -3k/(-7) = 3k/7
Slope of B = -2/1 = -2

(A)
For A and B to be parrallel, their slopes are equal.
3k/7 = -2
k = -14/3

(B)
For A and B to be perpendicular, their slopes multiply to -1
3k/7 * (-2) = -1
-6k/7 = -1
k = 7/6

(C)
Put y = 0 in A:
3kx - 7(0) - 10 = 0
3kx - 10 = 0
x = 10/(3k)

Put y = 0 in B:
2x + 0 - 7 = 0
2x - 7 = 0
x = 7/2

For A and B to have same x-intercept,
10/(3k) = 7/2
20 = 21k
k = 20/21


Hope it helps! ^^

1. X-intercept = -5 (When y=0 , 2x+10=0 -->x=-5)
slope = 2/5 (Rewrite the equation --> y =(2/5)x+2)

2.
3kx-7y-10=0 --> y=(3k/7)x-10/7
2x+y-7=0 -->y=-2x+7

(A) 3k/7 =-2
k=-14/3

(B) (3k/7 )*(-2 )=-1
k=7/6


(C) y=(3k/7)x-10/7 -- > x-intercept =10/3k
y=-2x+7-- >x-intercept =-7/2

-7/2=10/3k
k= -20/21