# Algebra 5.3 Writing Linear Equations Given Two Points.

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Algebra 5.3 Writing Linear Equations Given Two Points

Point Slope Form (PS) Today we will use this formula to find the equation of a line when you are only given two points on the line. Yesterday you learned to use this formula to find the equation of a line when you were given the slope and one point.

Writing an Equation of a Line from Two Points STEPS 1.Use the slope formula to find the slope m from the two points 2.Plug one of the points and m into the point slope (PS) formula 3.Simplify to slope-intercept (SI) form

(2, 2) (3, -4) Step 1: Compute slope Step 2: Use PS Form Step 3: Simplify to SI Form y + 4 = -6x + 18 -4 y = -6x + 14 Check with both points: Using (3, -4) 2 = -6(2) + 14-4 = -6(3) + 14 2 = 2-4 = -4 y = -6x + 14

Now you try. Write the equation of the line through the two given points. (2, -3) and (-3, 7) m = -2 PS: y +3 = -2(x – 2) or y – 7 = -2(x + 3) SI: y = -2x + 1

Write the equation of the line through the two given points. (-1, -2) and (2, 6) m = SI: PS:

Perpendicular Lines 90 Perpendicular lines have slopes that are the opposite of the reciprocal of each other m = -3 m = 1/3

Write the equation of the line perpendicular to the given line and passing through the given point. Perpendicular to y = -4x + 6 and passing through (0, 2) m = ¼ SI: y = ¼x + 2 PS: y – 2 = ¼(x – 0)

Homework pg. 288 #18-32, 36-41, 45-47, 58-60 Graph Paper