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College Algebra 2.1
 

College Algebra 2.1

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    College Algebra 2.1 College Algebra 2.1 Presentation Transcript

      • Slope-intercept form for equation of a line
      • Slope formula
      • Write equation of Line
      • Parallel and Perpendicular lines
      2.1 Linear Equations in 2 Variables
    • A. Slope-intercept form for equation of a line
      • y = mx + b
      • So if it looks like y = 3x – 4, then the slope is ____ and the y-intercept is (0,____).
    • Something for calc:
      • The meaning of the slope:
      • I’m standing on the graph. If I take 1 one-unit step to the right (positive direction on the x-axis), how high or low do I need to step? That’s the slope. See drawing:
    • B. Slope Formula
      • If you are given 2 points on the line, then you can find m (slope of the line) by labeling the ordered pairs (x 1 , y 1 ) and (x 2 , y 2 ) and using this formula:
    • Find the slope of the line passing through (3,4) and (5,7)
      • m =
      • Try: Find slope of line thru (-2,0) and (3,1)
      • Find slope of line thru (-1,2) and (2,2)
      • Find slope of line thru (3,4) and (3,1)
    • MEMORIZE
      • Slope of a __________________line is ___________.
      • Slope of a ___________________ line is ___________.
    • C. Writing the Equation of a Line
      • Whenever it starts with “write the equations of the line…” your answer should look like y = ____ x + ____.
      • All you need to do is figure out what m is and what b is.
    • How to find m?
      • They could tell you what it is equal to. That is nice when that happens.
      • If you know to ordered pairs, you could use the slope formula:
      • They might give a clue about what it is parallel or perpendicular to. We will talk more about that later.
    • How to find b:
      • They could say “the y-intercept is equal to..”
      • They could give you a point that looks like (0,__). If zero is the x-value, then b is its partner.
      • Or you can figure out what b is algebraically, like I ill show you on the next slide.
    • Find the equation of the line that goes through the point (1,-2) and has a slope of 3.
      • 1 st draw form: y = ____ x + _____
      • We know m: y = 3x + _____ Still need b!
      • You can plug in 1 for x and -2 for y, in order to find b.
    • Find the equation of the line passes thru (-2,3) and (0,1)
    • Try these:
      • Find the equ. Of the line passing thru (0, -10) and (-4, 0)
      • Find the equ. Of the line w/ slope 2 passing thru (-1, -1).
    • Find the equation of the line passing thru (4,2) and (4,-1).
      • But it still has an equation!
    • Find the equation of the line passing thru (2,3) and (-1,3).
      • But it still has an equation!
    • Memorize!
      • If the slope is undefined, the line is _____________, which means the equ will look like “x = ____”
      • If the slope is zero, the line is _____________, which means the equ will look like “y = ____”
    • Try these:
      • Find the equation of the line that goes thru (-1, 6) and (-1,0)
      • Find the equation of the line that goes thru (2,-2) and (3, -2)
    • D. Parallel and Perpendicular lines
      • Two lines are P______________ if their slopes are _______________________.
      • Two lines are P_______________ if their slopes are ________________________.
      • If the slope of one line is 3, and the slope of another line is -1/3, they are ________________.
      • If the slope of one line is 2/3, and the slope of another line is 2/3, they are ________________.
      • If the slope of one line is 2/3, and the slope of another line is -3/2, they are ________________.
      • If the slope of one line is ½ and the other is 2, they are NEITHER parallel nor perpendicular.
    • Find the equ of the line that passes thru (1,2) and is parallel to y=3x– 7.
    • Find the equation of the line that is perpendicular to y = 4x – 1 and goes thru (0,7).
    • Hey what about this one (maybe from part A really):
      • Find the slope of y + 5x = 8
      • Watch out for that.
    • You try:
      • Find the slope and y-intercept of 2x–3y = 6
      • Find the slope and y-intercept of 2x-y = 4