NOTES:
Use the equation y = mx + b where m is the unit rate and b is the one-time flat fee
1. Answer:
[tex]\begin {array}{c||c|c|c|c}x&0&1&2&3\\ y&70.00&70.20&70.40&70.60\\\end{array}[/tex]
Step-by-step explanation:
coffee maker costs $70 - this is a one-time flat fee
it costs $0.20 per cup of coffee - this is the unit rate
y = 0.20x + 70
y = 0.20(0) + 70 → y = 0.00 + 70 → y = 70.00
y = 0.20(1) + 70 → y = 0.20 + 70 → y = 70.20
y = 0.20(2) + 70 → y = 0.40 + 70 → y = 70.40
y = 0.20(3) + 70 → y = 0.60 + 70 → y = 70.40
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2. Answer:
[tex]\begin {array}{c||c|c|c|c}x&1&2&3&4\\ y&4.50&6.00&7.50&9.00\\\end{array}[/tex]
Step-by-step explanation:
shoes costs $3.00 - this is a one-time flat fee
it costs $1.50 per game of bowling - this is the unit rate
y = 1.50x + 3.00
y = 1.50(1) + 3.00 → y = 1.50 + 3.00 → y = 4.50
y = 1.50(2) + 3.00 → y = 3.00 + 3.00 → y = 6.00
y = 1.50(3) + 3.00 → y = 4.50 + 3.00 → y = 7.50
y = 1.50(4) + 3.00 → y = 6.00 + 3.00 → y = 9.00
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3. Answer: Negative
Step-by-step explanation:
As the x-values increase, the y-values decrease. Opposite directions results in a negative slope.
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4. Answer: Gym A → y = 20x + 50 Gym B → y = 25x + 30
Step-by-step explanation:
Use the slope formula: [tex]m = \dfrac{y_2-y_1}{x_2-x_1}[/tex]. Then choose ONE of the points and input the point (x₁, y₁) and slope (m) into the Point-Slope formula: y - y₁ = m(x - x₁) and solve for y.
Gym A: (x₁, y₁) = (1, 70) and (x₂, y₂) = (2, 90)
[tex]m=\dfrac{90-70}{2-1} = \dfrac{20}{1} = 20[/tex]
y - 70 = 20(x - 1)
y - 70 = 20x - 20
y = 20x + 50
Gym B: (x₁, y₁) = (1, 55) and (x₂, y₂) = (2, 80)
[tex]m=\dfrac{80-55}{2-1} = \dfrac{25}{1} = 25[/tex]
y - 55 = 25(x - 1)
y - 55 = 25x - 25
y = 25x + 30
