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Lesson 5.6 Point-Slope Form of the Equation of a Line

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43210 In addition to level 3.0 and above and beyond what was taught in class, the student may: · Make connection with other concepts in math · Make connection with other content areas. The student will understand that linear relationships can be described using multiple representations. - Represent and solve equations and inequalities graphically. - Write equations in slope-intercept form, point-slope form, and standard form. - Graph linear equations and inequalities in two variables. - Find x- and y- intercepts. The student will be able to: - Calculate slope. - Determine if a point is a solution to an equation. - Graph an equation using a table and slope-intercept form. With help from the teacher, the student has partial success with calculating slope, writing an equation in slope- intercept form, and graphing an equation. Even with help, the student has no success understanding the concept of a linear relationships. Learning Goal #1 for Focus 4 (HS.A-CED.A.2, HS.REI.ID.10 & 12, HS.F-IF.B.6, HS.F- IF.C.7, HS.F-LE.A.2): The student will understand that linear relationships can be described using multiple representations.

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Point-Slope Form of the Equation of a Line A line that passes through the point (x 1, y 1 ) with a slope of m. The point-slope form of the equation of the line is: y – y 1 = m(x – x 1 ) There is a difference between (x 1, y 1 ) and (x, y). –(x 1, y 1 ) is a specific point on the line. –(x, y) represents ANY point on a line.

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A line is passing through the points (-3, 6) and (1, -2). Write the equation of a line in Point-Slope Form. Step 1: Find the slope. m = y 2 -y 1 = -2 – 6 = -8 = -2 x 2 -x 1 1 – - 3 4 Step 2: Substitute one point, (-3, 6) and the slope into the Point-Slope Form equation: y – y 1 = m(x – x 1 ) y – 6 = -2(x - - 3) y – 6 = -2(x + 3)

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Change from Point-Slope Form to Slope-Intercept Form Write an equation of the line that passes through (2, 3) with a slope of – ½. Substitute into Point-Slope Form. y – y 1 = m(x – x 1 ) y – 3 = - ½(x – 2) Simplify the equation to put it into slope- intercept form. y – 3 = - ½x + 1 y = - ½x + 4

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Which equation would you use? Slope-Intercept, Standard, or Point-Slope Form The line passes through the points (1, 3) and (-2, 4). Point-slope because a point is given and a slope can be determined. The line has a slope of -4 and has a y- intercept of -12. Slope-intercept form because a slope and the y-intercept are given.

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