Drill #18 Find the x- and y– intercepts of the following equations in standard form, then graph each equation: 1. 2x – 2y = 6 2. -3x + 4y = 12 3. 2x + 3y = 8

Formulas from Standard Form* If an equation is in standard form Ax + By = C Then: X- intercept = C/A Y- Intercept = C/B Slope = -A/B

2-3 Slope Objective: To determine the slope of a line, to use the slope and a point to graph an equation and to determine if two lines are parallel, perpendicular, or neither.

Slope Intercept Form of a Linear Equation* y = mx + b m = slope b = y – intercept To graph an equation in slope intercept form: 1. Plot the y- intercept 2. Use the slope to plot a second point Example: y = ½ x – 2

Slope Uphill (+) Downhill ( - )

(1.) Slope** Slope: The ration of the change in vertical units to the change in horizontal units (RISE OVER RUN). The formula for the slope m of the line passing through and is given by . That is the change in the y coordinate (RISE) over the change in the x coordinate (RUN)

Classwork 2-3 Study Guide #1 – 3

Slope Examples* Find the slope of the line passing through the following points: Ex1: (5, 2) and (-2 , 3) Ex2: (-2, -1) and ( -1, 3)

Classwork 2-3 Study Guide #4 – 6

Slope* Find the value of r… Determine the value of r so that a line through the points has the given slope: Ex3: (3, r ) , ( -2, 1 ) m = 2 Ex4: ( -3 , 6) , ( r, 12) m = -¾

Using a Point and the Slope to Graph* 1. Plot the point (on a coordinate plane) 2. Use the slope (rise over run) to plot a second point. 3. Draw a line through the two points. Example: Graph a line that passes through (-2, -1) with a slope of 2.

Finding the Slope of Linear Equations* Standard Form: Ax + By = C Slope = - A/B Slope Intercept: y = mx + b Slope = m

(2.) Parallel Lines and (3.) Perpendicular Lines** Parallel Lines: In a plane, non-vertical lines with the same slope are parallel. Perpendicular Lines: In a plane, two oblique lines are perpendicular if and only if the product of their slopes is -1.

Parallel and Perpendicular Lines* Parallel Lines Have the same slope. To determine if two lines are parallel, find the slope of both lines. If they are the same they are parallel. Perpendicular Lines Product of slopes is -1 To determine if two lines are perpendicular, find the slope of both lines. Multiply the slopes together. If the product is -1 they are perpendicular.

Determine if the following lines are parallel, perpendicular, or neither: ex1. y = 3x + 3 y = -3x – 1 ex2. y = -2x + 1 y = ½ x – 2 ex3. y = 2 y = -½