Unit 2 – Linear Equations & Inequalities

Unit 2 – Linear Equations & Inequalities Topic: Writing & Graphing Linear Functions Materials needed for notes:Pencil& paper Flip book Journal

Things I expect you to remember from Algebra 1 that I do not explain in this PowerPoint • Slope-intercept form of a linear equation. • Graphing a linear function given: • A point on the line & the slope of the line. • The function of the line in slope-intercept form. • Using the slope formula (I will give you the formula in a couple slides, but I expect you to remember how to use it). • Using the graph of a line to write a function in slope-intercept form.

Things you should remember from Algebra 1 but that I KNOW you need to be reminded of • Identifying a linear function from data. • Standard form of a linear equation. • Recognizing standard form & graphing a line given a function in standard form. • The equations for horizontal & vertical lines. • Using data to write a linear function in slope-intercept form. • The relationship in the slopes of parallel & perpendicular lines.

Formulas for Linear Functions (put these on a note card) • Slope formula • (x1, y1) & (x2, y2) are coordinates for 2 points on the line • Standard form of a linear function • A, B, C  R, A & B cannot both be 0 • Point-slope form of a linear function • x1, y1 represent the coordinates of a point on the line • Can be used to find the equation of a line in slope-intercept given slope & a point, or two points

Identifying Linear Functions From Data • Linear functions have one & only one output value for every input value. • Rate of change (slope) between dependent variable and independent variable is constant.

Identifying Linear Functions From Data +2 +2 +2 +3 +6 +9 Rate of change is not constant. Data represents a function, but not a linear function.

Identifying Linear Functions From Data +2 +2 +2 +0 +0 +0 Rate of change is constant. Data represents a linear function.

Identifying Linear Functions From Data Two different outputs for the same input. Data does not represent a function.

Graphing Linear Functions in Standard Form • Use standard form to determine x- & y-intercepts. • Set y = 0 & solve for x to find x-intercept. • Set x = 0 & solve for y to find y-intercept. • Plot the intercepts and graph the line they form.

Horizontal & Vertical Lines • Horizontal lines have m = 0 • No rise, just run • y-value is constant so equation is always y = b, where b = y-intercept • Example: write the equation for the given line • y = 5

Horizontal & Vertical Lines • Vertical lines have undefined slope • Rise, but no run (can’t divide by 0) • x-value is constant so equation is always x = a, where a = x-intercept • Example: write the equation for the given line • x = –7

Parallel & Perpendicular Lines • Parallel Lines • Two lines whose slopes are equal. • Perpendicular Lines • Two lines whose slopes are negative reciprocals. • The product of the slopes of perpendicular lines is -1. • EXCEPTION: A horizontal line (m = 0) is perpendicular to a vertical line (m is undefined).

JOURNAL ENTRY • TITLE: Checking My Understanding: Writing & Graphing Linear Functions • Review your notes from this presentation & create and complete the following subheadings: • “Things I already knew:” Identify any information with which you were already familiar. • “New things I learned:” Identify any new information that you now understand. • “Questions I still have:” What do you still want to know or do not fully understand?

Homework • Textbook Section 2-3 (pg. 110): 22-40 even • Textbook Section 2-4 (pg.121): 12-18 even, 19-22 • Due 9/6 (B day) or 9/7 (A day)

Unit 2 – Linear Equations & Inequalities