You have already done half of it. Now substitute for x1 = 4 and y = 5
y - 5 = 6/7(x - 4)
Multiply everything by 7 to remove fractions
7y - 35 = 6(x - 4)
7y - 35 = 6x - 24
-6x + 7y = -24 + 35
-6x + 7y = 11
Some people prefer a positive number in front of x so multiply by -1
6x - 7y = -11
You can check the answer by testing it works for both of the original points
6x4 - 7x5 = 24 - 35 = -11 true
6x-3 - 7x-1 = -18 - -7 = -11 true
-48:4=-12
-12*5=-60
Hope it helps
y= x^2 - 6x-7
Vertex = -b /2a
b= -6
a= 1
-(-6)/2(1)= 3
x= 3
Use the substitution method to find y
y= (3)^2-6(3)-7
(3)(3)-18-7
9-25
y= -16
Vertex is (3, 16)
Find x- intercept (y= 0)
y= x^2 - 6x-7
(x-7)(x+1)
x-7= 0
Move -7 to the other side. Sign changes from -7 to 7
x-7+7= 0+7
x= 7
x+1= 0
Move +1 to the other side. Sign changes from +1 to -1
x+1-1= 0-1
x= -1
Answer :B. Vertex: (3, -16); Intercepts: x=-1,7
-3(2x-3)<3
(-3(2x-3))(-1)<3(-1)
3(2x-3)>-3
(3(2x-3))/3>-3/3
2x-3>-1
2x-3+3>-1+3
2x>2
2x/2>2/2
x>1
