For the equation -4y = 8x whay is the constant of variation
1 answer:
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Answer:
Amy has 12 5¢ coins
Step-by-step explanation:
Let <em>x</em> represent 20¢ coins and <em>y</em> represent 5¢ coins.
Amy has four more 20¢ coins than 5¢ coins. Hence:
And the total value of all her coins is $3.80. Thus:
This yields a system of equations:
We can solve by substitution. Substitute the first equation into the first:
Distribute:
Combine like terms:
And divide both sides by 0.25. Hence:
Thus, Amy has 12 5¢ coins.
Using the first equation:
Substitute:
Thus, Amy has 16 20¢ coins.
In conclusion, Amy has 12 5¢ coins and 16 20¢ coins.
Answer:
m = -3
b = 9
y = -3x + 9
Step-by-step explanation:
Let us solve the question
∵ The line passes through points (4, -3) and (3, 0)
∵ The rule of the slope is m =
∵ (x1, y1) and (x2, y2) are 2 points on the line
∴ x1 = 4 and y1 = -3
∴ x2 = 3 and y2 = 0
→ Substitute them in the rule of the slope to find it
∵ m = =
= -3
∴ m = -3
∵ The form of the equation of the line is y = m x + b
→ Substitute the value of m in the form of the equation.
∴ y = -3x + b
→ To find b substitute x and y by the coordinates of the point (3, 0) or (4, -3)
∵ x = 3 and y = 0
∴ 0 = -3(3) + b
∴ 0 = -9 + b
→ Add 9 to both sides
∴ 9 = b
∴ b = 9
→ Substitute the value of b in the equation
∵ y = -3x + 9
∴ The equation of the line is y = 3x + 9