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Notes Algebra Section 2.6 Date ______

Writing Equations in Point-Slope Form Form

Point-Slope Form:

A linear equation written in the form ___y - y1 = m(x - x1)___ is in ____point-slope form_. The line passes through the point (x1, y1) and the slope of the line is _m_.

Algebra: Graph:

EX1) Writing an equation using a slope and a point.

Write in point-slope form and equation of the line that passes through the point (-6, 1), with slope ⅔. y - y1 = m(x - x1)

●  Write the point-slope form y - 1 = ⅔ [x - (-6)]

●  Substitute ⅔ for m, -6 for x1 and 1 for y1. y - 1 = ⅔ (x + 6)

●  Simplify

●  Check by substituting in -6 for x and 1 for y. 1-1 = ⅔ (-6) + 4

0 = -4 + 4 = 0

You try: Write on your whiteboard first, when it is correct, write it in your notes.

Write the equation of the line in point-slope form with the given slope and point.

1.  (1,2): m= -4 2. (7,0): m=1 3. (-8, -5); m=-¾

y -2 = -4(x - 1) y - 0 = 1(x - 7) y - (-5) = -¾ [x - (-8)]

y = x - 7 y + 5 = -¾ (x + 8)

EX2) Writing an Equation using two points

Write in slope-intercept form an equation of a line that passes through the points (2, 4) and (5, -2) y2 - y1 = -2 - 4 = -6 = -2

x2 - x1 5 - 2 3

Find the slope using the slope formula:

Then use the slope and one of the points y - 4 = -2 (x - 2)

to write an equation of the line. y - 4 = -2x + 4

y = -2x + 8

Write the equation in slope-intercept form.

EX3) Real-Life Application

You finish parasailing and are being pulled back to the boat. After 2 seconds, you are 25 feet above the boat. You are descending at a rate of 10 feet per second.

a). Write and graph an equation that represents

your height y (in feet) above the boat after x seconds.

y - 25 = -10 (x - 2)

y - 25 = -10x + 20

y = -10x + 45

b). At what height were you parasailing?

The descent starts when the time, x, is 0 seconds, so it started at 45 feet.

You try: Write on your whiteboard first, when it is correct, write it in your notes.

Write in slope-intercept form an equation of a line that passes through the given points.

4. (-2, 1), (3, -4) 5. (-5, -5), (-3, 3) 6. (-8, 6), (-2, 9)

y = -x -1 y = 4x + 15 y = ½ x + 10

7. What if in EX3), you were 35 feet after 2 seconds? Write and graph an equation the represents your height y, in feet above the boat after x seconds.

y = -10x + 55