Assessing Fit and Using the Line

You will be able to:

• Judge a good fit from a poor fit
• Recognize when a line should not be drawn
• Predict from a line and write its equation

Learning Objectives for This Lesson

By the end of this lesson, you will be able to:

1. Assess fit by how close points are to the line
2. Recognize when a linear model is not appropriate
3. Use a fitted line to make predictions
4. Write and use the equation

Are Both of These Lines Equally Good?

Both slope up. Both have a fitted line. Are both lines equally trustworthy?

Tight Scatter Versus Wide Scatter

Tight cluster: a good fit. Wide spread: a poor fit.

Fit Means Closeness to the Line

• Good fit: points cluster tightly around the line
• Poor fit: points spread far from the line
• Fit is about scatter, not about direction

The Highway-Band Picture of Fit

• Imagine a band centered on the line
• Narrow band holds the points → good fit
• Wide band needed → poor fit

Don't Force a Line on a Curve

• A straight line misses a curved pattern
• High on the ends, low in the middle
• Should we draw this line at all?

No Trend Means No Line

• Random scatter has no direction to capture
• There is no trend for a line to summarize
• Drawing a line here would invent a pattern

Steep Is Not the Same as Good

• Steep line, wide scatter → poor fit
• Shallow line, tight scatter → good fit
• Slope is rate; fit is closeness

Remember y = mx + b

You already know this from algebra:

• is the slope — rise over run
• is the y-intercept — where the line crosses the axis

Predicting a Value From the Line

• Find , go up to the line, read
• Prediction: about 76; actual scores were 74 and 78

Quick Check: Predict at 2.5 Hours

Use the same line. A student studies 2.5 hours.

Read the predicted score off the line before advancing.

Finding the Slope From Two Points

Pick two points on the line — say (1, 57) and (4, 79) — and compute rise over run.

Reading the Intercept and Writing the Equation

Step 1: Slope

Step 2: Read the y-intercept:

Step 3:

Far Predictions Break the Model Down

• Inside the data range → trustworthy
• Far outside → unreliable
• — impossible, scores cap at 100

Your Turn: Finish the Equation

A fitted line passes through and .

1. Find the slope
2. Then write the full equation

Work the slope first, then advance for the next step.

Which Predictions Can You Trust?

Two plots have fitted lines.

• Plot A: points hug the line tightly
• Plot B: points spread widely

Whose predictions are more reliable, and why?

What If the Data Curve?

A scatter plot shows a clear curved pattern.

A classmate fits a straight line. What should they conclude instead?

Your Turn: Assess and Write the Equation

A new scatter plot with a fitted line is given.

1. Judge the fit: good or poor, and why
2. Pick two points and write

Do both steps on your own before comparing.

Three Traps to Avoid When Using Lines

Steep means good: steepness is rate, not fit quality
Line on curves: don't force a straight model on curved or trendless data
Trusting far predictions: the line is reliable only near the data

What the Line Buys You

✓ Fit tells you whether to trust the line
✓ The equation lets you compute with it
✓ Only a straight line on linear data earns either

Coming Up Next: Interpreting the Equation

Next, in 8.SP.A.3, you'll dig into what the slope and intercept mean in context — like "1.5 cm of plant growth per hour of sunlight" — and how to tell a safe prediction from a reckless one.