Represent two quantitative variables on a scatter plot, fit a linear model, and interpret slope and intercept in context (NC.M1.S-ID.6, S-ID.7).

What this topic is asking

NC.M1.S-ID.6 asks you to plot two quantitative variables on a scatter plot, describe the form and strength of the relationship, and fit a linear function to data that look linear, using it to solve problems. NC.M1.S-ID.7 asks you to interpret the slope and intercept of that linear model in context. This is two-variable numerical data modeled with a line.

Describing a scatter plot

Three things describe the pattern.

Fitting and using a line of best fit

A line of best fit summarizes a linear pattern and lets you predict.

Interpreting slope and intercept (S-ID.7)

The line's parts carry meaning in context.

• Slope $m$: the predicted change in $y$ per one-unit increase in $x$ (the rate). In $y = 15x + 100$, sales rise about \15$ per degree.
• y-intercept $b$: the predicted $y$ when $x = 0$. In $y = 15x + 100$, predicted sales at $0$ degrees are \100$.

Interpreting these is the same skill as reading a linear model, now applied to data.

How the NC Math 1 EOC examines this topic

• Multiple choice. Describe direction and strength, or interpret slope or intercept.
• Gridded response. Use a line of best fit to predict a value.
• Technology-enhanced. Match scatter plots to descriptions, or plot a fitted line.

Scatter plots lead directly into correlation and causation, where strength is quantified by the correlation coefficient, and they handle numerical pairs in contrast to the categorical pairs of two-way tables.

Why a line turns data into prediction

A scatter plot alone shows a trend, but a fitted line turns that trend into a usable rule: plug in an $x$ and read out a predicted $y$. The slope and intercept are what make the rule meaningful, the slope says how fast $y$ changes with $x$, and the intercept anchors the line. This is why S-ID.7 emphasizes interpretation in context: a slope of $15$ is not just a number, it is "\15$ more in sales per degree." The model is trustworthy within the range of the data but risky far beyond it, since the linear pattern may break down. Understanding the line as both a summary of the data and a predictor is the central idea, and it links statistics back to the linear functions strand.

Try this

Q1. A line of best fit is $y = -2x + 30$. Interpret the slope. [1 point]

• Cue. $y$ decreases by about $2$ for each one-unit increase in $x$ (negative rate).

Q2. Using $y = 3x + 5$, predict $y$ when $x = 10$. [1 point]

• Cue. $y = 3(10) + 5 = 35$.