Question

judy can decorate 3 cakes in 5 hours. which graph has a slope that best represents the number of cakes per hour judy can decorate?
there are four graphs labeled a, b, c, d for cake decorating, with y - axis as number of cakes (ranging from 0 to 30) and x - axis as time (hours, ranging from 0 to 10).

Explanation:

Step1: Calculate the rate (slope)

The rate of cakes per hour is the number of cakes divided by hours. Judy decorates 3 cakes in 5 hours, so the rate (slope) \( m=\frac{3}{5} = 0.6\) cakes per hour.

Step2: Analyze each graph's slope

• Graph A: Let's check the slope. For \( x = 10\) hours, \( y\) (cakes) is around 6? Wait, no, wait. Wait, the slope should be \( \frac{y}{x}\). If at \( x = 10\), \( y\) is 6? Wait, no, wait the first graph A: from (0,0) to, say, (10,6). Then slope is \( \frac{6}{10}=0.6\), which matches our rate. Wait, no, wait let's re - calculate. Wait, our rate is \( \frac{3}{5}=0.6\) cakes per hour. So in \( x\) hours, \( y = 0.6x\). Let's check each graph:
• Graph A: Let's see, when \( x = 5\), \( y\) should be \( 0.6\times5 = 3\), which matches (since 3 cakes in 5 hours). Let's check the end - point. At \( x = 10\), \( y=0.6\times10 = 6\). Looking at graph A, the line goes from (0,0) to (10,6), so slope \( \frac{6 - 0}{10 - 0}=0.6\), which is our rate.
• Graph B: If we assume at \( x = 10\), \( y\) is 18? Then slope \( \frac{18}{10}=1.8\), which is not 0.6.
• Graph C: At \( x = 10\), \( y = 30\), slope \( \frac{30}{10}=3\), not 0.6.
• Graph D: The slope is steeper, not 0.6.

Wait, maybe I misread the graphs. Wait, the first graph (A) has a line that goes from (0,0) and at \( x = 10\), \( y = 6\). So slope \( \frac{6}{10}=0.6\), which is equal to \( \frac{3}{5}\) (since \( \frac{3}{5}=0.6\)). Let's verify with the given rate: 3 cakes in 5 hours, so the equation is \( y=\frac{3}{5}x\). So when \( x = 5\), \( y = 3\); when \( x = 10\), \( y = 6\). Looking at graph A, this seems to match.

Answer:

A. Cake Decorating graph with slope 0.6 (the first graph, A)