اختبار اختيار من متعدد تفاعلي: Equation for a line that closely fits the data and prediction
This section covers the topic of scatter plots and lines of best fit. Students will learn how to find the equation for a line that closely fits a data set and use it to predict values that are not present in the original data set. The exercises include interpreting the slope and y-intercept within real-world contexts like sports participation, tip earnings, and temperature effects.
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اختبار شهادة تدريبي مؤقت للصف والمادة والفصل نفسه.
اختر إجابة واحدة لكل سؤال. عند الاختيار ستظهر النتيجة فورًا: الأخضر صحيح، والأحمر خطأ، وسيظهر تفسير الإجابة مباشرة إن كان متوفرًا. وبعد آخر سؤال ستظهر الدرجة النهائية تلقائيًا.
The scatter plot shows the number of girls that participated in high school sports. Write an equation in slope-intercept form for the line of fit that is drawn. Then interpret the slope and y-intercept.
Explanation
Looking at the graph, the line crosses the y-axis at 2.8. Choosing a point like (20, 3.3), the slope is (3.3 - 2.8) / (20 - 0) = 0.5 / 20 = 0.025. Therefore, the equation is y = 0.025x + 2.8.
Question 2
Points: 1
The scatter plot shows the tips different restaurant servers earned one night. Write an equation in slope-intercept form for the line of fit that is drawn. Then interpret the slope and y-intercept.
Explanation
The line of fit starts at the origin (0,0), so the y-intercept is 0. Using the point (100, 20), the slope is 20 / 100 = 0.2. The equation is y = 0.2x.
Question 3
Points: 1
The scatter plot shows the relationship between the number of times a cricket chirps and the current temperature. Write an equation for the line of fit. Then use it to make a conjecture about the temperature when there are 40 cricket chirps.
Explanation
The line has a y-intercept at 30. Using point (40, 70), the slope is (70 - 30) / 40 = 1. The equation is y = x + 30. At 40 chirps (x=40), y = 40 + 30 = 70.
Question 4
Points: 1
The scatter plot shows the results of a survey about age and daily time spent playing video games. Which equation best represents the line of fit?
Explanation
The line of fit has a negative slope and starts at a y-intercept of 90. Based on the data points, a slope of -0.8 accurately describes the downward trend of the line.
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