2You will need the worksheet that goes along with this power point presentation, a pencil, aruler, and a piece of graph paper. Readand follow directions carefully. At the end ofThe presentation, you should know somethingabout the slopes of parallel lines and theslopes of perpendicular lines.
3REVIEW: Parallel lines (//) are lines that never intersect. Perpendicular lines () are lines that intersect to formright angles.
4SLOPEOne nice thing about slope is that it’s a concept you already know aboutfrom everyday life. People talk about the slope of hills; golf commentatorsdiscuss the gentle slope of putting greens. So experience tells you thatslope has to do with steepness. In math, slope has a specific, technicalmeaning:It means the steepness of lines on the coordinate plane.From life, you also have a sense of what steepness means. For example,after climbing two hills, you should be able to say which one was steeper(at least your leg muscles will tell you the next day). But math, exactscience that it is, allows you to measure steepness with perfect, numericalprecision.
5In algebra, the symbol for slope is the letter m. Here are some other things to know about slope:• A horizontal line, having no steepness,has a slope of 0.• A vertical line, having absolute steepness,has a slope that is undefined.• Lines that rise from left to right have apositive slope.• Lines that fall from left to right have anegative slope.
6What is the formuula for the slope of a line? OR The formula for the slope of a line is:risey2 - y1ORm =m =runx2 - x1where (x1, y1) and (x2, y2)are the coordinates of anytwo points on the line.(x2, y2)(x1, y1)
7Find the slope of the lines passing through these points. Show your work and write your answers on your piece ofpaper (#6).a) (4, 3) and (9, 6)b) (8, -2) and (6, 5)- 3= 3/5= -7/2c) (-10, 5) and (15, -20)d) (-3, -6) and (8, 7)
8Count the slope when you are given a line on a graph. To get from one point to the other on the line, you have to go up 2 and over 3 to the right,so the slope is ⅔.Over 3Up 2
9Find the slope of the line graphed below. Notice that to get fromone point to the next onthis graph you have togo down 2 and to theright one, so the slopeis -2/1.
10If you are given a point on a line and the slope of the line, you can graph the line.• Graph the point that you are given.This will be the starting point.• Start at the point you graphed andcount the slope.Graph the line through (-6, -5)with slope 3/2.
11The line through (-4, 2) with slope of 4/5. Use the graph by #7 on your worksheet to complete thefollowing graphs:The line through (-4, 2) with slope of 4/5.b) The line through (1, 2) with slope of -3/4.c) The line through (3, -2) with slope of 3.
12On your graph for #8, graph the line through (2, 3) with a slope of ¾. On the same graph, graph the equation y = ¾ x + -4.Click here if you needto review how to grapha linear equation.What do you notice about the two lines that you graphed?What do you notice about the slopes of the two lines?
13On the graph for #9, graph AB and CD. Click here if youforgot how tofind slope.Find the slope of each line.The slope of AB = 6/5 5/6 -5/6 -6/5The slope of CD = 6/5 5/6 -5/6 -6/5Click on the correct answer.What do you notice about the two lines that you graphed?What do you notice about the slopes of the two lines?
14What can you conclude about the slopes of parallel lines? The slopes of parallel lines are equal or the same!!The slope of a line is 1/3. What is the slope of a lineparallel to this one?3-1/31/41/3
15Line b has a slope of 2/3 and line d has a slope of 1/3. Is b // d? yesnoE (2, -11), F (4, -5), G (2, 8) and H (5, 17)Without graphing, determine if EF// GH.Show all work on your paper next to #10. (think slope)Click here if you forgothow to find slope.
16Graph the line through (-5, -8) with a slope of ½. (Do this on the graph for #11).On the same graph, graph the line that passes through (-9, 7)with a slope of -2.What do you notice about the two lines?Is there a relationship between the slopes?
17Graph the two equations below on the graph for #12. y = 2/3 x + 2Click here if you needhelp graphing linearequations.y = -3/2 x + -3What do you notice about the two lines?What do you notice about the slopes? (Hint: try multiplyingthem)
18What do you notice about the two lines? L (-4, 0) M (0, 3) N (1, 7) P (4, 3)Graph LM and NP on #13.What do you notice about the two lines?Click on the slope of LM : ¾ 4/3 -3/4 -4/3Click on the slope of NP : ¾ 4/3 -3/4 -4/3What do you notice about the slopes of these twoperpendicular lines? Hint: try multiplying them again.Click here if you forgothow to find slope.
19What can you conclude about the slopes of perpendicular lines? The product of the slopes of perpendicular lines is -1.Notice that if the slope of the original line is ¾, to find theslope of the perpendicular line (-4/3) you flip the originalslope (reciprocal) and make it the opposite.The slope of a line is -5/7. What is the slope of theperpendicular line? (flip and opposite)5/7 7/5 -5/7 -7/5
20Line a has a slope of -1/2 and line c has a slope of 2. Is a b? yesnoQ (-3, -2) R (9, 1) S (3, 6) T (5, -2)Without graphing, determine if QR ST. Think slope.Show all work on your paper next to #14.Click here if you forgothow to find slope!
21Slopes of parallel and perpendicular lines The equation for a line is y = ¼ x + 5.What is the slope of a line parallel to this one?¼ /1 -1/ / /1What is the slope of a line perpendicular to this one?¼ /1 -1/ / /1
22Complete #15 & #16on your worksheet.Did you complete #15 & #16?
23Okay, I get it! The slopes of parallel lines are equal! And the slopesof perpendicularlines are oppositereciprocals (theirproduct is -1)!For perpendicularlines I just flip theslope and changeto its opposite.That’s what I said!
24Complete #17 & #18on the worksheetand then you arefinished!
27Review - graphing a linear equation: To graph the equation y = ½ x + 2:1. Graph the y-intercept (the point where the linecrosses the y-axis) - (0,2)Count the slope - rise over run(½)Draw a line throughthe pointsReturn to previous slide
28Try Again.Remember that the slopes of parallel lines are equal.
29Try Again. Remember that the slopes of perpendicular lines have a product of -1. So, take the original slope andflip it. Then make it the opposite.
30Return to previous slide. What is the formuulafor theslope of a line?The formula for the slope of a line is:risey2 - y1ORm =m =runx2 - x1where (x1, y1) and (x2, y2)are the coordinates of anytwo points on the line.(x2, y2)(x1, y1)Return to previous slide.