Section 2.2 – Linear Equations Def: Linear Equation – an equation that can be written as y = mx + b m = slope b = y-intercept.

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Presentation transcript:

Section 2.2 – Linear Equations Def: Linear Equation – an equation that can be written as y = mx + b m = slope b = y-intercept

x & y intercepts – where a graph crosses the x or y-axis. Ex: Find the intercepts of the following equations: ◦ a) 3x + 2y = 12 ◦ b) 4x – 9y = 18 ◦ c) 2x + 5y = 14

◦ d) y = 3x + 4 ◦ e) y = 2x – 9 ◦ f) Def: Standard Form: Ax + By = C SF: 3x – 2y = 12 Non-SF: y = 2x – 8

The equation 3x + 2y = 120 models the number of passengers who can sit in a train car, where x is the number of adults and y is the number of children. 1) Graph the equation. 2) Explain what the x & y intercepts are. 3) Find the domain and range.

Def: Slope – the ratio of vertical change to horizontal change. Find the slope between the points: 1) A(3, -8) and B(-2, 9) 2) C(-6, -1) and D(4, -13)

Point-Slope Form: Slope-Intercept Form: y = mx + b Standard Form: Ax + By = C

Ex: Find the slope and all 3 forms of the line that passes through the points: 1) A(7, -2) and B(4, 1) II) C(8, 6) and D(4, 9)

Graph the following equations: 1) 4x – 2y = 12 (Standard) II) (Slope-Intercept) III) (Point-Slope)

Find the slope of the lines: A) y = 3x + 4 B) y + 3 = 2(x – 5) C) 3x + 4y = 12 D) 2x – 9y = 27 E) Ax + By = C

Given a line, put into other two forms: 1) 3x + 2y = 8 II) Vertical & Horizontal Lines - slope

Parallel Lines – have same slope Perpendicular Lines – have opposite reciprocal slope Find the slope parallel & perpendicular to: 1) m = 2/3 2) m = -4 3) m = -0.3

Find the equation of a line parallel to 2x – 3y = 12 passing through the point (4, -6) Find the equation of a line perpendicular to 3x + 5y = 20 passing through the point (-1, 9)