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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