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Published byMabel McDonald Modified over 4 years ago

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Bell Work Solve for “y” 1.) 3x – 2y = -8 2.) 5x – y + 12 = 3x + 10 3.) 3x – 4y = -7y – 12

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Slope of a Line Slope – The ratio of the change in value of the y-coordinates over the change in value of the x-coordinates for any two points on a line. Slope is represented by the letter “m”.

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Slope Formulas:

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Bell Work 1. -5x + 4y = -16 2. 3x – 6y = 12 + 2x 3. 2(-2x – y) = 3x + 4

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Special Slopes Horizontal lines have a slope of zero. (Zero is in the top of the fraction.) Vertical lines have a slope that is undefined. (Zero is in the bottom of the fraction.)

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Bell Work Determine the slope using the two points given. Determine the slope using the two points given. 1.) (3, 6), (1, 3)2.) (-2, 4), (3, 2) 3.) (-1, 3), (-1, 5)4.) (-2, 4), (-3, 4)

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Rise over Run Triangle May determine the slope of a line by determining the rise and run from two points on the line. May determine the slope of a line by determining the rise and run from two points on the line. A line has a positive slope if the line is rising from left to right. A line has a positive slope if the line is rising from left to right. A line has a negative slope if the line is going down from left to right. A line has a negative slope if the line is going down from left to right.

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Steps for doing Rise over Run Triangle 1.) Find two points on the line. 2.) Create a right triangle using the two points. 3.) Determine the rise and the run and put in fraction form (rise on top, run on bottom). 4.) Determine if the slope is positive or negative. 5.) Reduce the fraction if possible.

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Slope-Intercept Form y = mx + b m = slope b = y-intercept

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Slope-Intercept Form An equation is in slope-intercept form if the equation is solved for “y”. An equation is in slope-intercept form if the equation is solved for “y”. The number in front of “x” is the slope. The number in front of “x” is the slope. The number by itself is the “y- intercept.” The number by itself is the “y- intercept.” “b” is used to represent y-intercept. “b” is used to represent y-intercept. y = mx + b y = mx + b

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Graphing a Line using the slope and a point 1. Get the equation in slope-int. & identify “m” & “b”. 2. Plot the y-intercept. 3. Plot the second point using the slope from the y-intercept. a) Top # determines how many you go up or down from the point. Positive goes up. Negative goes down. b) Bottom # determines how many you go to the right. 4. Connect the points.

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Bell Work Get “y” by itself. 1. 3x – 2y = 6 2. ½ y – 2x = -3 3. 3x + 4y – 5 = 5x + 4

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Graphing Using Intercepts x-intercept – The point where a line crosses the x-axis. (x, 0) is the ordered pair. y-intercept – The point where a line crosses the y-axis. (0, y) is the ordered pair.

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2x + 3y = -6 Get the equation in standard form. To find the x-intercept, substitute 0 for “y” in the equation given and find what “x” is equal to. To find the y-intercept, substitute 0 for “x” in the equation given and find what “y” is equal to.

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To graph the line, plot the x-intercept and the y-intercept and then connect the dots.

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