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 Solve each equation for y. 2. m = –1, x = 5, and y = –4 b = –6 b = x – 2y = 8 y = 2x – 4

Graph lines and write their equations in slope-intercept and point-slope form. Classify lines as parallel, intersecting, or coinciding. Objectives

(1,2) (5,4) THINK… If you don’t have a graph, how could you use the coordinates (x,y) to find the rise and run?

EXAMPLE 2: Graphing Lines using slope-intercept form ***The equation is in slope-intercept form, y = mx + b. ***The slope is m = ___ and the y-intercept is b = ___. Step 1: Graph the y-intercept Step 3: Draw a line through the points with arrows. 2

Writing Equations of Lines: Given 2 Points Step 1: Find the slope between the two points. Step 2: Choose any one point as (x 1, y 1 ). Step 3: Insert m, x 1, and y 1 into the point-slope equation. point-slope form. The y-intercept is not clear from this picture, so we can’t use slope- intercept form, we’ll have to use point-slope form.

HORIZONTAL LINE: Horizontal lines have a slope of ____. Every point on the horizontal line through (2, 4) has a y-coordinate of ____. The equation of the line is ________. VERTICAL LINE: Vertical lines have a slope of _____. Every point on the vertical line through (2, 4) has an x-coordinate of _____. The equation of the line is _________ undefined y = 4 0 Equations of Horizontal and Vertical Lines Let’s look at some points on the Horizontal Line (3, 4)(5, 4)(0, 4)(-2, 4) Let’s look at some points on the Vertical Line 4 2 x = 2 (2,-1) (2,0) (2,2) Horizontal Lines: y = # Vertical Lines: x = #

Determine whether the lines are parallel, intersect, or coincide. Example 3A: Classifying Pairs of Lines y = 3x + 7, y = –3x – 4 The lines have different slopes, so they intersect.

Determine whether the lines are parallel, intersect, or coincide. Example 3B: Classifying Pairs of Lines Solve the second equation for y to find the slope-intercept form. 6y = –2x + 12 Both lines have a slope of, and the y-intercepts are different. So the lines are parallel.