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Lesson 3-5: Slope

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. Slope: Steepness from one point to another Ratio of vertical change, Δ y, to horizontal change, Δ x. Written as:.

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Lesson 3-5: Slope

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  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 y2 or y1 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 ofthrough point (-4,-10) Start w/point slope formula Substitute from problem Distribute simplify Solve for y (slope-intercept)

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

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

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

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