Task Sets: Know that straight lines are widely used to model relationships between two quantitative variables - Common Core Math - Grade 8

Recall / Warm-Up

$A scatter plot whose points rise from the lower left to the upper right with no line drawn$

A scatter plot shows a clear upward linear trend. Why might we draw a single straight line through the cloud of points?

The line summarizes the overall trend, giving a simple model of how the two variables are related

The line must pass exactly through every data point

Real data always falls perfectly on a straight line

A fitted line passes through the points $(1, 4)$ and $(5, 12)$ . What is the slope of the line?

$A scatter plot with a solid line through the middle of the points and a dashed line sitting above most points$

Two students draw a straight line through the same scatter plot. One line has 8 points above and 1 below; the other has 5 above and 4 below. Which line is better balanced for an informal fit?

The line with 5 points above and 4 below, because the points are split roughly in half

The line with 8 above and 1 below, because it sits near the top points

They are equally good - balance does not matter

Fluency Practice

$A scatter plot whose points rise steeply at first then level off, forming a curve$

A scatter plot is shown. Is a straight line an appropriate model for this data?

No - the points follow a curved path, so a straight line would miss the pattern

Yes - a straight line is always appropriate for any scatter plot

Yes - because the points generally go up, a straight line fits perfectly

$A scatter plot with a solid line through the middle of an upward band of points$

A line has been drawn through a scatter plot. Using the criteria for a good informal fit, how well does this line fit the data?

Good fit - the line follows the upward trend and the points split roughly evenly above and below

Poor fit - a fitted line must pass through every data point, and this one does not

Poor fit - the line should connect the lowest and highest points

$Two scatter plots each with an upward line - Plot A has points tightly clustered on the line, Plot B has points spread widely around it$

Two scatter plots each have a fitted line drawn through them. In which plot is the line a better fit?

Plot A, because the points cluster tightly around the line

Plot B, because its points are more spread out

They fit equally well, because both lines have the same slope

Complete the sentence about assessing fit. When the data points cluster tightly around the fitted line, the fit is ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ . When the points are widely scattered far from the line, the fit is ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ .

quality when points are close (good or poor):

quality when points are far (good or poor):

$A scatter plot with a fitted line crossing the grid intersection at x equals 4, y equals 5$

A fitted line is drawn on a scatter plot. Use the line to predict the value of $y$ when $x = 4$ . Read the prediction from the line.

Exercises: Fitting and Assessing Lines on Scatter Plots

Recall / Warm-Up

Fluency Practice