1. Section P.5 Linear Equations in Two Variables 1.Slope: can either be a ratio or a rate if the x and y axis have the same units of measures then the slope has no units and is a ratio. It can be defined as:  rise over run  the change in y divided by the change in x  vertical change horizontal change  Δy = y 2 -y 1 Δx x 2 -x 1, where x 2  x 1 (rule #9)

2. if the x and y axes have different units of measure, then the slope is a rate or a rate of change o Ex. see graph p. 49 Ex. find the slope of the line passing through the points (-2,0) and (3,1) There are four cases for slope: i.+ slope: line rises left to right ii.-slope: line falls left to right iii.0 slope: line is horizontal iv.undefined slope: line is vertical

3. 2. Equations of Lines (rule #10) General form: Ax + By + C = 0 Vertical line: x = a Horizontal line: y = b Slope-intercept form: y = mx + b Point slope form: y-y 1 = m(x-x 1 ) Two-point form: y-y 1 = y 2 -y 1 (x-x 1 ) x 2 -x 1 Ex. write the equation of the line passing through the points (1,3) and (2,5) in point slope form and in the general form. (Graph on calculator) Ex 6 p. 53 note: think of data given as an ordered pair

4. 3. Parallel and Perpendicular Lines two lines are parallel iff their slope are equal m 1 =m 2 two lines are perpendicular iff their slopes are negative reciprocals m 1 = -1/m 2 Ex. Find the slope intercept form of the line that passes through the point (2,-1) and is parallel to the line 2x-3y=5.