Question

1. a baker has already made 10 cakes. she can make the same number of cakes each hour, which she does for 5 hours. sketch the graph of the relationship between the number of cakes made and time.

Explanation:

Step1: Define Variables and Initial Point

Let \( x \) be time in hours (independent variable) and \( y \) be number of cakes (dependent variable). At \( x = 0 \) (start time), \( y = 10 \) (already made cakes), so the initial point is \( (0, 10) \).

Step2: Determine the Relationship Type

The baker makes a constant number of cakes per hour, so the relationship is linear. Let \( r \) be the rate (cakes per hour). The equation is \( y=10 + r x \), where \( x\in[0,5] \).

Step3: Identify End Point

After \( x = 5 \) hours, the number of cakes is \( y = 10+5r \). But since we just need to sketch the graph, we know it's a straight line from \( (0, 10) \) to \( (5, 10 + 5r) \). However, since the rate \( r \) is constant (same number per hour), the graph is a straight line with positive slope starting at \( (0, 10) \) and ending at \( (5, 10 + 5r) \). For sketching, we plot the initial point \( (0, 10) \) on the y - axis (since at time 0, 10 cakes are made) and then draw a straight line to the point corresponding to \( x = 5 \) hours. The x - axis is time (from 0 to 5) and y - axis is number of cakes (starting at 10 and increasing linearly).

Answer:

The graph is a straight line segment. It starts at the point \((0, 10)\) (on the \(y\) - axis, since at time \(x = 0\) hours, the number of cakes \(y=10\)) and extends to the point \((5,10 + 5r)\) (where \(r\) is the number of cakes made per hour) with a positive slope (since the number of cakes increases as time increases). To sketch it, plot the point \((0, 10)\), then draw a straight line to the point corresponding to \(x = 5\) hours (the \(y\) - coordinate at \(x = 5\) will be \(10\) plus \(5\) times the number of cakes made per hour).