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Lesson 2-2 Linear Equations • Linear function – a function whose graph is a line. • A linear function is represented by a linear equation. ex) y = 2x + 3 A solution of a linear equation is an ordered pair. y = 3x + 2 Because the value of y depends on the value of x, y is called the DEPENDENT VARIABLE and x is called the INDEPENDENT VARIABLE • When graphing a linear equation make a t-chart. • y = 3x + 2 • To be sure you didn’t make a mistake graph at least three points. • y-intercept – point where the line crosses the y axis. • What is the value of x at the y-intercept. • x-intercept – point where the line crosses the x axis. • What is the value of y at the x-intercept. Slope Slope = vertical change = rise = y2 – y1 horizontal change run x 2 – x1 Find the slope of the line that goes through the points ( -2, -2) and (4, 2) • Standard Form of a linear equation – is in the form Ax + By = C • A must be positive. • A, B, and C are integers. You can graph a linear equation in Standard Form by using the intercepts • When an equation is in standard form the slope = -A/B • 2x + 3y = 7 • Slope-intercept form y = mx + b slope y-intercept • Graph from Slope intercept form – Put the y-intercept on the graph and use the slope to find other points • Write in standard form an equation of a line with slope 2 through (4, -2) • If you are given two points and asked to write an equation, Find the slope first, then write the equation. • (5,0) (-3, 2) • Point-Slope Form The line through point (x1, y1) with slope m has the equation: y – y1 = m(x – x1) • Standard Form: Ax + By = C • Point Slope Form: y – y1 = m(x – x1) • Slope Intercept: y = mx + b Horizontal lines • m=0 • y is constant Vertical Lines • m is undefined • x is constant Parallel Lines m=m b1 = b2 Perpendicular Lines • m2 is the opposite reciprocal of m1 • m1 = -1/ m2 • 2-64 even pg 67 - 68