Question
The table shows the numbers x
of hours spent studying and the test scores y
of several students.
The line of best fit is y=5x+61
a. Interpret the slope and y-intercept of the line of best fit.
b. Approximate the test score of a student who spends 3 hours studying.
(5 points)
a. The slope is
and the y-intercept is
. So , a student who studies 0 hours is expected to earn a
on the test, and the score increases by about
points per hour spent studying.
b. about
points
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of hours spent studying and the test scores y
of several students.
The line of best fit is y=5x+61
a. Interpret the slope and y-intercept of the line of best fit.
b. Approximate the test score of a student who spends 3 hours studying.
(5 points)
a. The slope is
and the y-intercept is
. So , a student who studies 0 hours is expected to earn a
on the test, and the score increases by about
points per hour spent studying.
b. about
points
Skip to navigation
Answers
GPT-4o mini
Let's analyze the line of best fit \( y = 5x + 61 \).
### a. Interpretation of the Slope and Y-Intercept
- **Slope (5)**: The slope of the line is 5, which means that for each additional hour spent studying, a student's test score is expected to increase by about 5 points.
- **Y-Intercept (61)**: The y-intercept of the line is 61, which means that if a student spends 0 hours studying (x = 0), their expected test score would be 61 points.
Putting this together:
- The slope is **5** and the y-intercept is **61**. So, a student who studies 0 hours is expected to earn **61** on the test, and the score increases by about **5** points per hour spent studying.
### b. Approximate Test Score for 3 Hours of Studying
To find the approximate test score for a student who spends 3 hours studying, we substitute \( x = 3 \) into the equation:
\[
y = 5(3) + 61
\]
\[
y = 15 + 61
\]
\[
y = 76
\]
So, a student who studies for 3 hours is expected to score about **76** points.
### Summary:
- a. The slope is **5**, the y-intercept is **61**. A student who studies 0 hours is expected to earn **61**, and the score increases by about **5** points per hour.
- b. About **76** points.
### a. Interpretation of the Slope and Y-Intercept
- **Slope (5)**: The slope of the line is 5, which means that for each additional hour spent studying, a student's test score is expected to increase by about 5 points.
- **Y-Intercept (61)**: The y-intercept of the line is 61, which means that if a student spends 0 hours studying (x = 0), their expected test score would be 61 points.
Putting this together:
- The slope is **5** and the y-intercept is **61**. So, a student who studies 0 hours is expected to earn **61** on the test, and the score increases by about **5** points per hour spent studying.
### b. Approximate Test Score for 3 Hours of Studying
To find the approximate test score for a student who spends 3 hours studying, we substitute \( x = 3 \) into the equation:
\[
y = 5(3) + 61
\]
\[
y = 15 + 61
\]
\[
y = 76
\]
So, a student who studies for 3 hours is expected to score about **76** points.
### Summary:
- a. The slope is **5**, the y-intercept is **61**. A student who studies 0 hours is expected to earn **61**, and the score increases by about **5** points per hour.
- b. About **76** points.