Lesson 1: The Equation of a Linear Function

Which variable represents slope in the slope-intercept form?

Which variable represents the y-intercept in the slope-intercept form?

If you know the location of one point on a line and that the slope of the line is -3, how can you locate another point on the line?

How do you find the horizontal intercept of a function?

Slope
y-intercept
horizontal intercept

A.CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

F.IF.7a Graph linear and quadratic functions and show intercepts, maxima, and minima.

SAT questions related to slope: 8-3-13,6-3-1,5-4-7,8-3-19,7-4-17,1-3-6,3-4-8;
graphing: 6-3-5;
functions: 3-4-4, 5-4-2, 6-4-25

Lesson Description This lesson focuses on the algebraic techniques used to write the equation of a line in slope-intercept form (f(x) = mx + b). Students will practice two primary scenarios: Vertical and Horizontal Constraints: Reinforcing how to write equations for special cases (e.g., a line with a slope of 0 or an undefined slope passing through a specific point).

Purpose
The purpose of Section 10.1 is to teach reverse engineering. Previously, students were given an equation and asked to find its properties; now, they are given properties and asked to find the equation. This is a foundational skill in data modeling—if you know the rate at which a cost is rising and you know the cost today, you can create the formula to predict the cost at any point in the future. This move toward "model building" is a key requirement for success in MAT 137 (Intermediate Algebra).

Jamil has 500 songs on his smartphone. He joins a music club that lets him download 30 songs per month for a monthly fee. the number of songs that Jamil could eventually have if he does not delete any songs is represented by y = 30x + 500 for x months.

Plotting slope from the origin as opposed to the y-intercept

Have students plot a line with the given slope that goes through the origin. Then have them move that line up the y-axis until it goes through the y-intercept.

Use "you try" pg 223 and practice problems to assess students' understanding of the lesson concepts