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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 slopeintercept 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 A, B, C R, A & B cannot both be 0 y2 y1 m x2 x1 Standard form of a linear function Ax By C 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 y y1 m( x x1 ) 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 x f(x) 0 -1 2 2 +3 +2 +2 +2 4 8 +6 6 17 +9 Rate of change is not constant. Data represents a function, but not a linear function. Identifying Linear Functions From Data x f(x) -2 3 0 3 +0 Rate of change +2 +2 +2 2 3 +0 4 3 +0 f ( x) 0 Rate of change is constant. Data represents a linear x 2 function. Identifying Linear Functions From Data x f(x) -3 3 -1 0 1 -3 -1 -6 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)