Week 4 — Linear Functions & Their Graphs

Welcome to your Week 4 Start Here page.

Why this matters

A straight line is how a nursing student reads a drip that adds the same amount each hour and how a small-business owner prices an order with a base fee plus a per-item charge. Read its slope and its starting value, and you can predict the next number and check it.

In plain language

Some things change by the same amount every time, like a price that goes up 3 dollars for each topping you add. This week you learn to read that kind of steady change as a straight line on a graph. You will measure a line's slope (how steep it is, or how much it rises for each step to the right). You will find its intercepts (the places where the line crosses the two axes). Last, you will learn to tell when two lines run side by side forever and when they cross at a perfect square corner.

• Already covered: Week 1 set the sign rules; Week 2 solved linear equations; Week 3 named functions such as g(x) = 3x + 4.
• This week: the straight line itself — slope, slope-intercept form, point-slope form, intercepts and standard form, and parallel and perpendicular lines.
• How they connect: a line's equation is a function like the ones from Week 3, and every rearranging step this week is a Week 2 move.
• Where we're going next: Week 5, Systems of Linear Equations & Inequalities, puts two lines on one graph and asks where they meet.

Focus

What two numbers describe a straight line, and how do you find them, use them, and check them?

By the end of this module, you should be able to:

• [ ] find a slope from two points and say what it means in units
• [ ] read m and b from y = mx + b and write a line from two points
• [ ] find both intercepts and graph a line from them
• [ ] tell parallel from perpendicular lines by their slopes

To-do

Plan your week

1. Read Chapter 4 (about 40 minutes), then the lecture and slides.
2. Work the lecture tutorial (60–90 minutes) and the practice set (about 20 minutes).
3. Do the Model/Build Studio (about 90 minutes), the discussion, and the assignment.
4. Take the quiz.

This week's checkpoint: find the slope and the y-intercept of the line through (−1, 4) and (3, −4), and check both points.

You've got this

Take it in order, and ask your instructor early if a step snags.

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