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Slopes, Parallel Lines, Perpendicular Lines, Equations of Lines, Graphing Functions and Examining Coefficients

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Loretta Violante

on 11 May 2013

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Transcript of Slopes, Parallel Lines, Perpendicular Lines, Equations of Lines, Graphing Functions and Examining Coefficients

What is slope? There are four different types of slope... POSITIVE SLOPE A positive slope is a line that slants upward from left to right. example: NEGATIVE SLOPE A negative slope is a line that slopes downward from left to right. To remember negative slope, keep in mind that "N" stands for Negative! Zero Slope A slope that lays horizontally/ is parallel to the "x" axis is a zero slope. UNDEFINED SLOPE An undefined slope is a line that lays vertically, or straight up and down. How can we express slope? Slope can be expressed as... y=mx+b y x b= m= y x y x 2 2 1 1 - - Graphing Lines in Slope Intercept Form Slope Intercept Form: y=mx+b m is the slope b is the y-intercept Graphing An Equation example: y= 2x+3 Plot the y-intercept. Plot the slope To plot the slope, use rise over run example: change the slope 2x into 2 1 Draw a line that runs through the points that you plotted above. Draw arrows on the ends of your line. Examples of Slope y=4x+2 y=6x-5 2 Game 2: Algebra vs. The Cockroaches Game 1: Hoop Shot www.crctlessons.com/slope-game.html Some fun slope games to try... hotmath.com/hotmath_help/games/kp/kp_hotmath_sound.swf Slope, Parallels Lines, Perpendicular Lines, Equations of Lines, Graphing Functions and Examining Coefficients Loretta Violante 8th grade loretta violante math, Mr.Schmidt Slope is the rate of change in a line. It is always defined from left to right and represented by m. Equations of Lines Slope Intercept Form (taught in the previous slide) y=mx+b Slope intercept form is used when you know what both the slope and the y-intercept are. Vertical Line Form Point Slope Form Horizontal Line Form Standard Form Vertical Lines have no slope. Their slope has a rise but no run. These vertical lines slopes have zero denominators and are undefined. Example: The line pictured above has a slope of -3 0 Point slope form can be used when you know a point on the line and the slope. y-y =m(x-x ) 1 1 example: In this graph, we can see that one point is (1,2) and the slope is up 2 over 1. Therefore, we can use point slope form to solve this equation. x=2 (or any other number) y=2 (or any other number) Horizontal Lines have a zero slope. These lines have a run but no rise Ax+By=C Example: Standard Form: 3x+y=3 Parallels and Perpendiculars Parallel Lines Perpendicular Lines an example of parallel lines... Lines that are parallel always have the same slope. They never intersect. Perpendicular Lines are two lines that intersect at a 90 degree angle. Perpendicular lines are negative reciprocal slopes. Two perpendicular lines are opposites. For example, if one line has a positive slope, its perpendicular line would be negative. Graphing Functions Each of these lines are parallel because they have the same slope: y=4x+5.8 y=4x-7 y=4x+2 y=4x-6.8943 How to find the negative reciprocal of a number: STEP EXAMPLE Flip the two numbers 3 4 3 4 Make the number negative 4 3 3 4 - In order to graph standard form, the equation can be turned into slope intercept form. Changed to Slope Intercept Form: y=3x+6 3x+y=3 -3x -3x Once changed to slope intercept form, the equation can be graphed. What are Linear Functions? A linear function is a straight line. As discussed previously, there are different kinds of slopes that functions can have. These include positive, negative, undefined and zero slope. How do you graph them? Also explained previously, functions can be graphed different ways. The five main ways are slope intercept, point slope, standard, vertical line and horizontal line form. POSITIVE SLOPE NEGATIVE SLOPE UNDEFINED SLOPE ZERO SLOPE Examining Coefficients What is a coefficient? Examining Coefficients A coefficient is the number in front of a variable or the number itself. examples: 6x the coefficient in this number is 6 34x + 2.5x the coefficients in this equation are 34 and 2.5 8y 2 the coefficient in this number is 8 Math Project, 2013 The symbol for parallel lines looks like the number 11 Once you know one point and the slope, you can plug these numbers into the above equation then convert it to slope intercept form.
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