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Point-Slope Formula

Point-Slope Formula. Writing an Equation of a line Using the Point-Slope Formula. The point-slope formula is given by where m is the slope of the line and is a known point on the line. Writing an Equation of a Line Using the Point-Slope Formula. m = 3 Point ( -2, -4 ). 3.

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Point-Slope Formula

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  1. Point-Slope Formula Writing an Equation of a line Using the Point-Slope Formula

  2. The point-slope formula is given bywhere m is the slope of the line and is a known point on the line.

  3. Writing an Equation of a Line Using the Point-Slope Formula m = 3 Point ( -2, -4 ) 3 -2 -4 -4 3 -2 The point-slope formula: Simplify. Because the final answer is required in slope-intercept form, simplify the equation and solve for y. y + 4 = 3(x + 2) y + 4 = 3x + 6 Apply the distributive property y + 4 – 4 = 3x + 6 -4 Subtract 4 from both sides. Slope-intercept form y = 3x +2

  4. Writing an Equation of a Line Through Two Points Points (-2, 5) and (4, -1) -1 5 -2 5 4 -1 4 -2 Find the slope 5 -1 -2 The point-slope formula: Simplify. Because the final answer is required in slope-intercept form, simplify the equation and solve for y. y – 5 = -1(x – (-2) y - 5 = -x + 2 Apply the distributive property y -5 + 5 = -x + 2 +5 Add 5 to both sides. Slope-intercept form y = -x + 3

  5. Write an Equation of a Line Parallel to Another Line Use the point-slope formula to find an equation of the line passing through the point(-1, 0) and parallel to the line y = -4x + 3, Write the final answer in slope-intercept form. Lets now apply the point-slope formula using m = -4 point = (-1, 0) 0 -4 -1 y = -4( x +1) y = -4x -4 m = -4 b = -4 y = mx + b What formula could we use to write the equation? Slope-intercept form y = mx + b Lets use the graph to find the equation. What is the slope and the y-intercept? y = -4x -4

  6. Write an Equation of a Line Perpendicular to Another Line Use the point-slope formula to find an equation of the line passing through the point (-3, 1) and perpendicular to the line 3x + y = -2. Write the final answer in slope-intercept form. The given line can be written in slope-intercept form as y = -3x -2. The slope of this line is -3. Therefore, the slope of a line perpendicular to the given line is ⅓ Point-slope formula 1 ⅓ (-3) Substitute m = ⅓ x₁ = -3, y₁ = 1 y – 1 = ⅓(x + 3) To write the final answer in slope-intercept form, simplify the equation and solve for y. y - 1 = ⅓x + 1 Apply the distributive property y = ⅓x + 2 Add 1 to both sides

  7. Different forms of Linear Equations:

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