These 22 problems practice Common Core standards 8.SP.A.2 and 8.SP.A.3. Judge how well a line fits a scatter plot, find the equation of a line from two points, and interpret slope and y-intercept in context.
The last six problems are word problems about predictions, outliers and models that stop making sense. Work from easiest to hardest.
Problem 1: Judge the fit
The scatter plot shows hours studied and quiz score for seven students. The line \(y=6x+52\) is drawn. Is the line a good fit? Explain.
Problem 2: Gap from the line
A line of fit for the study data is \(y=6x+52\). Student 3 studied 3 hours and scored 67. Student 6 studied 6 hours and scored 90. For each student, find the predicted score and say whether the actual score is above or below the line.
Problem 3: Slope from two points
A line of fit passes through \((10,5)\) and \((30,17)\). Find its slope.
Problem 4: Find the y-intercept
A line of fit has slope 6 and passes through \((2,64)\). Find its y-intercept.
Problem 5: Write the equation
A line of fit passes through \((1,10)\) and \((5,30)\). Write its equation in the form \(y=mx+b\).
Problem 6: A poor fit
The plot shows shoe size and test score for seven students, with the flat line \(y=77\) and dashed gaps. Is a line a good model for these data? Explain.
Problem 7: A curved pattern
The plot shows the height of a ball at different times , with the line \(y=6x+2\). Explain why a straight line is a poor model.
Problem 8: Sign of the slope
The line \(y=-2x+26\) models the value \(y\) (in thousands of dollars) of a used car that is \(x\) years old. Is the slope positive or negative? What does it mean?
Problem 9: Meaning of the intercept
For the model \(y=-2x+26\) in the car problem, find the y-intercept and explain what it means.
Problem 10: Predict a score
Use \(y=6x+52\) to predict the quiz score of a student who studies 4.5 hours.
Problem 11: Equation from the graph
The line of fit for a plant’s growth passes through \((0,4)\) and \((10,22)\). Write its equation, where \(x\) is days since planting and \(y\) is height in centimeters.
Problem 12: Meaning in context
The plant model is \(y=1.8x+4\). Explain what the slope and the y-intercept mean for the plant.
Problem 13: Predict plant height
Use \(y=1.8x+4\) to predict the plant’s height on day 7 and on day 15. Which prediction is more reliable? Explain.
Problem 14: Compare two lines
A data set has the points \((1,4)\), \((2,6)\), \((3,9)\), \((4,11)\) and \((5,14)\). Line P is \(y=2.5x+1.5\) and line Q is \(y=3x\). Add up the vertical gaps for each line. Which line fits better?
Problem 15: Slope in context
The model \(y=2x-108\) relates the temperature \(x\) (in \(^{\circ}\text{F}\)) to the cups of lemonade \(y\) sold. Explain what the slope means.
Problem 16: Is the intercept meaningful?
Find the y-intercept of \(y=2x-108\) and decide whether it makes sense for the lemonade stand.
Problem 17: Bike ride model
Priya’s bike ride data fit the line \(y=0.25x\), where \(x\) is minutes and \(y\) is miles. Explain what the slope and the y-intercept mean. Then convert the slope to miles per hour.
Problem 18: Bike predictions
Use \(y=0.25x\) to predict how far Priya rides in 45 minutes. Then find how long she needs to ride 9 miles.
Problem 19: Spot the outlier
The plot shows weeks of practice and free throws made (out of 40) for a player. The line is \(y=3x+10\). Identify the outlier and find its vertical gap from the line.
Problem 20: Phone battery
A phone’s battery percent \(y\) after \(x\) hours of video fits the model \(y=-12x+100\). (a) Explain the slope and intercept. (b) After how many hours does the model predict 28%? (c) Is the model reasonable for 12 hours? Explain.
Problem 21: Saving for a bike
Sofia’s savings fit the model \(s=15w+40\), where \(w\) is the number of weeks and \(s\) is dollars saved. (a) What does 15 mean? What does 40 mean? (b) Predict her savings after 10 weeks. (c) In how many weeks does the model predict $250?
Problem 22: Hot cocoa sales
A cafe recorded temperature \(x\) (in \(^{\circ}\text{F}\)) and cups of hot cocoa sold \(y\): \((30,95)\), \((40,78)\), \((50,66)\), \((60,48)\), \((70,36)\). A line of fit is \(y=-1.5x+140\). (a) Explain the slope. (b) Predict sales at \(45^{\circ}\text{F}\). (c) The model predicts 20 cups at what temperature? Is that prediction reliable?
See every chapter on the Grade 8 math page.