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Point Slope Form

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Point Slope Form

1. 1. Point-Slope Form
2. 2. What we Know so far…. Slope Intercept Form Where m is the slope and b is the intercept
3. 3. The New Stuff… Point- Slope Form Point- Slope form is: Where m is the slope and (x 1, y 1 ) is the given point
4. 4. Using Point-Slope Form We need the slope and a point: Plug it into the point-slope form From there you can simplify to slope-intercept form 1 2 4 3 5 -1 -2 -3 -4 -5 1 2 3 4 5 -1 -2 -3 -4 -5 (2,2)
5. 5. Write the Equation in Point-Slope Form Step 1: Plug it in
6. 6. Point Slope Form <ul><li>The equation for the non-vertical line is: </li></ul> Y  X y – y 1 = m (x – x 1 ) ( Point Slope Form ) <ul><li>Where m is: </li></ul>m =  Y (x 2 – x 1 ) Y X Y-axis X-axis  X = (y 2 – y 1 ) (x 1 ,y 1 ) (x 2 ,y 2 )
7. 7. Point Slope Form <ul><li>Let’s find the equation for the line passing through the points (3,-2) and (6,10) </li></ul>Mr Brown Honors Geometry  Y  X <ul><li>First, Calculate m : </li></ul>m =  Y (3,-2) (6,10) Y X Y-axis X-axis  X = ( 10 – -2 ) ( 6 – 3 ) 3 12 = = 4
8. 8. Point Slope Form <ul><li>To find the equation for the line passing through the points (3,-2) and (6,10) </li></ul>Mr Brown Honors Geometry  Y  X y – y 1 = m (x – x 1 ) Next plug it into Point Slope From : (3,-2) (6,10) y – -2 = 4 (x – 3 ) Select one point as P 1 : Let’s use (3,-2) The Equation becomes: Y X Y-axis X-axis
9. 9. Example 2: Point Slope Form <ul><li>Simplify the equation / put it into Slope Intercept Form </li></ul>Mr Brown Honors Geometry  Y  X y + 2 = 4 x – 12 Distribute on the right side and the equation becomes: (3,-2) (6,10) Subtract 2 from both sides gives. y = 4x – 14 Y X Y-axis X-axis y + 2 = 4 x – 12 -2 = - 2
10. 10. A Challenge Can you write the equation of a line in point-slope form that passes through (-3,6) and (1,-2)