Question

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tanya is having a bake sale and must bake cupcakes. she has cupcakes donated by a friend and after her first hour of baking, tanya has a total of 60 cupcakes. she has 84 cupcakes after the second hour of baking. tanya continues baking the same number of cupcakes each hour.
select the value to correctly complete the sentence
the graph for the number of cupcakes baked will have a slope of □ and a y-intercept of □

Explanation:

Step1: Find the slope (rate of change)

The slope represents the number of cupcakes baked per hour. After 1 hour, she has 60; after 2 hours, 84. The change in cupcakes is \( 84 - 60 = 24 \), and the change in time is \( 2 - 1 = 1 \) hour. So slope \( m = \frac{24}{1} = 24 \).

Step2: Find the y - intercept (initial number of cupcakes)

Let the equation be \( y = mx + b \), where \( y \) is total cupcakes, \( x \) is hours, \( m \) is slope, and \( b \) is y - intercept. Using \( x = 1 \), \( y = 60 \), and \( m = 24 \): \( 60 = 24(1)+b \). Solving for \( b \): \( b = 60 - 24 = 36 \). So the y - intercept is 36 (the initial number of donated cupcakes).

Answer:

Slope: 24, Y - intercept: 36