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Point-Slope Form: Linear Equations in Two Variables

Learn about point-slope form and how to write linear equations using this form. Explore examples and step-by-step instructions.

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Point-Slope Form: Linear Equations in Two Variables

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  1. Point-Slope Form Linear Equations in Two Variables

  2. What we Know so far…. Slope Intercept Form Where m is the slope and b is the intercept

  3. The New Stuff… Point- Slope Form Point- Slope form is: Where m is the slope and (x1, y1) is the given point

  4. Write the Equation in Point-Slope Form Step 1: Plug it in Point- Slope Form Slope – Intercept Form

  5. A linear equation written in the form y – y1 = m(x – x1) is in point-slope form. 1 1 1 2 2 2 Example:The graph of the equation y – 3 = -(x – 4) is a line of slope m = - passing through the point (4,3). y m = - 8 (4, 3) 4 x 4 8 The graph of this equation is a line with slope m passing through the point (x1, y1). Plot the point, then rise & run from there….

  6. Using Point-Slope Form 5 4 3 (2,2) 2 1 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5 We need the slope and a point: Plug them into the point-slope form Point – Slope Form

  7. Let m = 3, let (x1, y1)= (-2,5). y – 5 = 3(x – (-2)) y – 5 = 3(x + 2) Simplify into point-slope form Example: Write the point-slope form for the equation of the line through the point (-2,5) with a slope of 3. Use the point-slope form, y – y1 = m(x – x1), with m = 3 and (x1, y1)= (-2,5). y – y1 = m(x – x1)

  8. (2,-3) and (4,-2) Given two points, write the equation of a line in point-slope form Steps: 1. Find slope 2. Place a point and the slope in into point slope form 3. Point-Slope form Solve for y & get .. Slope-intercept form

  9. To write point-slope into slope-intercept: Simplify using distributive property, then move the constant to the right side & combine like terms

  10. m = Calculate the slope. 1 1 3 3 Point-slope form y – y1 = m(x – x1) 5 – 3 2 1 = - = - Use m = -and the point (4,3). -2 – 4 6 3 y – 3 = - (x – 4) 13 Slope-intercept form 3 y = - x + Example: Write the slope-intercept form for the equation of the line through the points (4,3) and (-2,5). Solve for y…

  11. A Challenge Can you write the equation of a line in point-slope form that passes through (-3,6) and (1,-2) m = Calculate the slope. 6 + 2 8 2 = - = - -3 – 1 4 1 y – y1 = m(x – x1) Use m = - 2 and the point (1,-2). y + 2 = - 2 (x – 1) Point-Slope Form y = -2(x – 1) - 2 y = -2x + 2 - 2 Slope-Intercept Form y = -2x + 0 y = -2x

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