6: Yes, it is linear. The constant rate of change is

, which you can make

. This simplifies to 15, so the constant rate of change is 15.
7. Yes, a proportional relationship exists because every output value is exactly three times every corresponding input value.
8. Yes, a proportional relationship exists because every output value is exactly

times the corresponding input value.
9. Yes, a proportional relationship exists because every y value is 7.5 times every corresponding x value, and if a line were to be drawn through the points, it would go through the origin (0,0).
Answer: y=-2x+8
Step-by-step explanation: Write a table of values where for every x y goes down 2 to find the y intercept (0,8) so it would be 8. The slope is -2 and that is all you need to write the equation.
Answer:
I think A
Step-by-step explanation:
Answer:
Step-by-step explanation:
1. 6x + 10 = 6x - 8
10≠-8
no solution
2. 6x + 8 = 2x - 6
4x + 8 = -6
4x = -14
x = -14/4= -7/2 one solution
3. 9x - 27 = 9x - 27
0 = 0 All real no. infinitely many solution
Answer:
Step-by-step explanation:
B(2,10); D(6,2)
Midpoint(x1+x2/2, y1+y2/2) = M ( 2+6/2, 10+2/2) = M(8/2, 12/2) = M(4,6)
Rhombus all sides are equal.
AB = BC = CD =AD
distance = √(x2-x1)² + (y2- y1)²
As A lies on x-axis, it y-co ordinate = 0; Let its x-co ordinate be x
A(X,0)
AB = AD
√(2-x)² + (10-0)² = √(6-x)² + (2-0)²
√(2-x)² + (10)² = √(6-x)² + (2)²
√x² -4x +4 + 100 = √x²-12x+36 + 4
√x² -4x + 104 = √x²-12x+40
square both sides,
x² -4x + 104 = x²-12x+40
x² -4x - x²+ 12x = 40 - 104
8x = -64
x = -64/8
x = -8
A(-8,0)
Let C(a,b)
M is AC midpoint
(-8+a/2, 0 + b/2) = M(4,6)
(-8+a/2, b/2) = M(4,6)
Comparing;
-8+a/2 = 4 ; b/2 = 6
-8+a = 4*2 ; b = 6*2
-8+a = 8 ; b = 12
a = 8 +8
a = 16
Hence, C(16,12)