Question

constructing graphs algebra 1 topic 1
lesson 1: overview and representing data homework/staying sharp page 1 of 5

1. practice look at the data in this table.

there appears to be a relationship between
the time a student spends studying for a test
and the grade the student makes on the test.

xaxis (time spent studying (hours))	yaxis (grade on test)
1	60
\\(1\frac{1}{2}\\)	70
\\(1\frac{3}{4}\\)	80
2	95

a. create a neutral graph to present the data. explain how you chose the scale
for your graph.

graph grid with \grade\ (y-axis: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100) and \time\ (x-axis: 0.5, 1, 1.5, 2, 2.5, 3) with some plotted points

copyright agile mind, inc. © content copyright charles a. dana center, the university of texas at austin

Explanation:

Step1: Analyze x - axis data

The x - axis data (time spent studying) values are $\frac{1}{2}=0.5$, $1$, $1\frac{1}{2} = 1.5$, $1\frac{3}{4}=1.75$, $2$. The range of x - values is from $0.5$ to $2$. So, we can choose a scale where each grid line on the x - axis represents $0.25$ hours. This way, we can plot all the x - values accurately. For example, $0.5$ (which is $\frac{1}{2}$) is 2 grid units (since $0.5\div0.25 = 2$), $1$ is 4 grid units ($1\div0.25=4$), $1.5$ is 6 grid units ($1.5\div0.25 = 6$), $1.75$ is 7 grid units ($1.75\div0.25=7$), and $2$ is 8 grid units ($2\div0.25 = 8$).

Step2: Analyze y - axis data

The y - axis data (grade on test) values are $50$, $60$, $70$, $80$, $95$. The range of y - values is from $50$ to $95$. We can choose a scale where each grid line on the y - axis represents $5$ points. This is because the data points have a difference of $10$ (from $50$ to $60$, $60$ to $70$, $70$ to $80$) and then a difference of $15$ (from $80$ to $95$). A scale of $5$ per grid line allows us to plot the points precisely. For example, $50$ is 10 grid units ($50\div5 = 10$), $60$ is 12 grid units ($60\div5=12$), $70$ is 14 grid units ($70\div5 = 14$), $80$ is 16 grid units ($80\div5=16$), and $95$ is 19 grid units ($95\div5 = 19$).

Step3: Plot the points

• For the point $(\frac{1}{2},50)$: On the x - axis, move to the position corresponding to $0.5$ hours (2 grid units if each grid is $0.25$), and on the y - axis, move to the position corresponding to $50$ (10 grid units if each grid is $5$) and mark the point.
• For the point $(1,60)$: On the x - axis, move to 1 hour (4 grid units), and on the y - axis, move to 60 (12 grid units) and mark the point.
• For the point $(1\frac{1}{2},70)$: On the x - axis, move to $1.5$ hours (6 grid units), and on the y - axis, move to 70 (14 grid units) and mark the point.
• For the point $(1\frac{3}{4},80)$: On the x - axis, move to $1.75$ hours (7 grid units), and on the y - axis, move to 80 (16 grid units) and mark the point.
• For the point $(2,95)$: On the x - axis, move to 2 hours (8 grid units), and on the y - axis, move to 95 (19 grid units) and mark the point.

Step4: Draw the graph

Connect the plotted points (or just leave them as individual points for a scatter - plot - like neutral graph) to show the relationship between study time and test grade. The x - axis is labeled "Time spent studying (hours)" and the y - axis is labeled "Grade on test".

Answer:

To create the neutral graph (scatter plot):

X - axis Scale Choice:

The time values are $\frac{1}{2},1,1\frac{1}{2},1\frac{3}{4},2$ (in hours). The minimum value is $\frac{1}{2}=0.5$ and the maximum is $2$. A scale where each grid square represents $0.25$ hours is chosen. This is because the data points have fractional values (like $\frac{1}{2},1\frac{1}{2},1\frac{3}{4}$) and a $0.25$ - hour scale allows us to plot each point accurately (e.g., $\frac{1}{2}$ hour is 2 grid squares, $1$ hour is 4 grid squares, etc.).

Y - axis Scale Choice:

The grade values are $50,60,70,80,95$. The minimum is $50$ and the maximum is $95$. A scale where each grid square represents $5$ points is chosen. This is because the grade differences are mostly multiples of $10$ (or $15$ for the last point), and a $5$ - point scale provides enough granularity to plot each grade (e.g., $50$ is 10 grid squares, $60$ is 12 grid squares, etc.).

Plotting Points:

• For $(\frac{1}{2},50)$: Locate $0.5$ on the x - axis (2 grid squares from the origin if each grid is $0.25$) and $50$ on the y - axis (10 grid squares from the origin if each grid is $5$), then mark the point.
• For $(1,60)$: Locate $1$ on the x - axis (4 grid squares) and $60$ on the y - axis (12 grid squares), mark the point.
• For $(1\frac{1}{2},70)$: Locate $1.5$ on the x - axis (6 grid squares) and $70$ on the y - axis (14 grid squares), mark the point.
• For $(1\frac{3}{4},80)$: Locate $1.75$ on the x - axis (7 grid squares) and $80$ on the y - axis (16 grid squares), mark the point.
• For $(2,95)$: Locate $2$ on the x - axis (8 grid squares) and $95$ on the y - axis (19 grid squares), mark the point.

The graph has the x - axis labeled "Time spent studying (hours)" and the y - axis labeled "Grade on test", with points plotted as described above.