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# College Algebra 2.1

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### College Algebra 2.1

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