1. Lesson 3-5: Slope Objectives: Students will: Find the slope of a line from 2 points Find the slope of horizontal and vertical lines Write equations for lines

2. Slope: Steepness from one point to another Ratio of vertical change, Δy, to horizontal change, Δx. Written as: Find the slope: Example 1: (3, 5) and (-2, 8) Example 2: (-5, 4) and (-1, -9) Can consider rise or run negative but not both!!! Doesn’t matter which points is called y 2 or y 1 as long as ordered pairs stay together

3. Review Slopes of horizontal and vertical lines Simply evaluate the ratio Horizontal lines: Vertical lines: H-Z- y = # V-N- X = #

4. To write an equation with a given slope passing through a given point (x,y) Rearrange the formula for slope as follows Get rid of fraction Called point-slope form

5. Example 3: Write an equation with a slope of through point (-4,-10) Start w/point slope formula Distribute simplify Substitute from problem Solve for y (slope-intercept)

6. Another Method Writing Equations using slope → y = mx + b Steps: 1)Plug in slope and given point 2)Solve for b 3)Write equation filling in numbers for “m” and “b”

7. y = mx + b 5=2(3) + b 5= 6 + b -1 = b y = 2x - 1 Example 4: Find b method Write an equation for the line through (3, 5) with slope 2 Start with slope-intercept Substitute from problem Simplify and solve for b Put m and b into slope-intercept form

8. Which method did you prefer? Why???