2.5 Linear Equations.

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Presentation transcript:

2.5 Linear Equations

Graphing using slope and y-intercept (section 2.4) Graphing using table Graphing using slope and y-intercept (section 2.4) Graphing using x-intercept and y-intercept (section 2.5) X-intercept y-intercept

To find x-intercept, set y = 0, solve for x To find y-intercept, set x = o, solve for y Ex1) 3x + 2y = 12

Ex2) y = -4x + 5 Ex3) x + (1/2)y = -8

Ex: y = 2x - 4, we have x-intercept (2, 0) y-intercept (0, -4) To graph a linear equation, find x-intercept and y-intercept, plot them then connect the points. Ex: y = 2x - 4, we have x-intercept (2, 0) y-intercept (0, -4) (2,0) (0,-4))

Standard Form of Linear Equation: Ax + By = C Slope-Intercept Form: y = mx + b Point-Slope Form: y – y1 = m (x – x1)

Two lines are parallel if they have the same slope Ex: y = 3x + 4 y = 3x - 2 Two lines are perpendicular if the product of their slopes = -1 (or one slope is the opposite reciprocal of the other slope). Ex: y = (1/3) x y = -3x - 2

Are these lines parallel, perpendicular, or neither? y = (-3/2)x + 4 2y + 3x = 1 y = 5x 5y + 15 = x 3) x + 3y = 3 3x = 1 + y

Horizontal line: slope = 0 Ex: y = 4 or y = -2 Vertical line: slope is undefined Ex: x = 4 or x = -2