2.3 Quick Graphs of Linear Equations and 2.4 Writing Equations of Lines The SLOPE INTERCEPT form of a line is y = mx + b STANDARD FORM OF A LINE: Ax + By = C where A, B, and C are integers and A > 0 y = −2x + 3 y= 2 x−3 3 2 1 y=− x+ 5 2 x-intercept: __________________ x-intercept: __________________ x-intercept: __________________ Standard Form:_______________ Standard Form:_______________ Standard Form:_______________ What formula can you use to generalize the slope of a line if the equation is given in standard form ? m = ______ 5x + 3y = -15 slope:______ y-intercept:___________ y = 3x x-intercept: __________________ x-intercept:_______ y=7 x-intercept: __________________ x = −4 x-intercept: __________________ 2.3 Quick Graphs of Linear Equations and 2.4 Writing Equations of Lines Graph then write an equation of the line that passes through the point ( -3, 4) and m = 1.) Slope-Intercept Form: y = mx + b 2.) Point-Slope Form: y − y1 = m( x − x1 ) 3.) Standard Form: Ax + By = C 4.) Given Two Points: Write the equation of the line that passes through (−2,−1) and (3,4) 5.) Write the equation of the line shown. State your answer in slope-intercept Form. 2 3 2.3 Quick Graphs of Linear Equations and 2.4 Writing Equations of Lines Writing Equations of Parallel and Perpendicular Lines. Parallel Lines: Two lines are parallel if and only if they have the same ___________. Perpendicular lines: Two lines are perpendicular if and only if their slopes are ___________________________ __________________ of each other. Key Questions: All types of vertical lines are parallel to what types of lines? _______________________ All types of vertical lines are perpendicular to what types of lines? _________________ Graph and use the slope formula tell whether the lines are parallel, perpendicular or neither. Line 1: through (−3,3) and (3,−1) Line 2: through (−2,−3) and (2,3) Write an equation of the line that passes through ( 2, -3) and is parallel to the line that passes through (3, 5) and (-1, -3) Write an equation of the line that passes through ( 3, 2) and is perpendicular to the line y = −3 x + 2 Write an equation of a line that passes through ( 3, -5) that is a.) perpendicular b.) parallel to the line x = 4. 2.3 Quick Graphs of Linear Equations and 2.4 Writing Equations of Lines

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