3.6 - Equations of Lines in the Coordinate Plane Please view the presentation in slideshow mode by clicking this icon at the bottom of the screen. Warm Up Substitute the given values of m, x, and y into the equation y = mx + b and solve for b. 1. m = 2, x = 3, and y = 0 2. m = –1, x = 5, and y = –4 Solve each equation for y. 3. 4x – 2y = 8 y = 2x – 4 b = –6 b=1 Objectives Graph lines and write their equations in slope-intercept and point-slope form. Classify lines as parallel, intersecting, or coinciding. For Instance… How can you use the THINK… (5,4) EXAMPLE 1: y-coordinates to get the rise (1,2) If you don’t have a of 2 units? 1) What is the slope of the line? Subtract! how could you 6 5 −−1 graph, 4 – 2the = 2coordinates = use 5 3 −−2 How can you find the run of 4 units? (x,y) to find the rise Subtract! 2) What is the the line between the points (4, -6) & 5 –slope 1 and = 4of run? (7,2)? 2 − −6 8 = 7 −4 3 EXAMPLE 2: Graphing Lines using slope-intercept form x What is the graph of y = + 2? ***The equation is in slope-intercept form, y = mx + b. for TIP 2 ***The slope is m = ___ andusing the y-intercept is b = ___. UP for positive or DOWN for negative. Step 1: Graph Rise the y-intercept Step 2: Find another point using for But ALWAYS Run to the m = 2. Go up 2, and 3 RIGHT! over 3. *REPEAT* Step 3: Draw a line through the points with arrows. Step 1: Find the slope between the two points. Writing Equations of Lines: The y-intercept is not Given 2 Points clear from this picture, can’t use slopeWhat issoanweequation of the line in the intercept form, we’ll figure athave thetoright? use point-slope form. m= = 5 −3 = 3 −−5 2 1 = = 8 4 Equation: Using Using 2 − 1 2 − 1 Step 2: Choose any one point as (x1, y1). 1 (-5,3): y – 3 = (x + 5) 4 1 (3,5): y – 5 = (x – 3) 4 …or… Step 3: Insert m, x1, and y1 into the point-slope equation. Equations of Horizontal and Vertical Lines HORIZONTAL LINE: 0 Horizontal lines have a slope of ____. Let’s look at some Every point on the horizontal line points on the through (2, 4) has a y-coordinate of Horizontal Line 4 ____. The equation of the line is ________. y=4 (-2, 4) (0, 4) VERTICAL LINE: undefined Vertical lines have slopeatofsome _____. Let’salook Every point on the vertical line points on the through (2, 4) has an x-coordinate Vertical Line 2 of _____. x=2 The equation of the line is _________ (3, 4) (5, 4) (2,2) (2,0) (2,-1) Horizontal Lines: y=# Vertical Lines: x=# Example 3A: Classifying Pairs of Lines Determine whether the lines are parallel, intersect, or coincide. y = 3x + 7, y = –3x – 4 The lines have different slopes, so they intersect. Example 3B: Classifying Pairs of Lines Determine whether the lines are parallel, intersect, or coincide. Solve the second equation for y to find the slope-intercept form. 6y = –2x + 12 Both lines have a slope of lines are parallel. , and the y-intercepts are different. So the

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# Lines in the Coordinate Plane