LINES 1. SLOPE 2. GRAPHING LINEAR EQUATIONS 3. WRITINGLINEAR EQUATIONS

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LINES 1. SLOPE 2. GRAPHING LINEAR EQUATIONS 3. WRITINGLINEAR EQUATIONS 4. PARALLEL & PERPENDICULAR Created by ﺠﻴﻄ for mathlabsky.wordpress.com Created by ﺠﻴﻄ for mathlabsky.wordpress.com

Slope of a Line Slope (gradient) is a ratio of the change in y (vertical change) to the change in x ( horizontal change) The slope, denoted by m, of the line through the points and Is defined as follows: Y ● ● Invers X

Find the slope of each segment (a, b, c and d)!  3 -5 6 -3 a b c d Find the slope of each segment (a, b, c and d)! Lines with positive slope rise to the right Lines with negative slope fall to the right

k h Find the slope of line k and h! Slope of line 4 Slope of line 6 4 8

Linear equations can be written in different forms : Standard form and slope-intercept form. Form Equation Slope Standard Slope-intercept Example : Equation Form Slope standard standard Slope-intercept Slope-intercept standard Slope-intercept HOME

Y X Graphing Linear Equations To draw the line we need two point determine a line. We can find the X-intercept and Y-intercept. Y X Example : graph the line 2x + 3y = 12 To find X-intercept, let y = 0 ● (0 , 4) Thus, (6 , 0) is a point on the line To find Y-intercept, let x = 0 ● (6 , 0) Thus, (0 , 4) is a point on the line HOME

Writing Linear Equations 1. An equation of the line that passes through the point and has slope m is : Example : Find an equation of the line through (1 , 3) and its slope 2 Solution :

2. An equation of the line that passes through the point and is : Example : Find an equation of the line through (-1 , 4) and (2 , -3) Solution : HOME

Parallel and Perpendicular Lines Two lines are parallel if and only if their slope equal If slope k1 = m1 and slope k2 = m2 Parallel Two lines are Perpendicular if and only if the product of Their slope = -1 If slope h1 = m1 and slope h2 = m2 Perpendicular

Example : check the two lines parallel or perpendicular and Solution : Let slope the first line is ,then Let slope second line is , then The line are not parallel The line are Perpendicular

Exercise, check the two line parallel or perpendicular HOME