Download Slope! - Signal Hill #181

Slope!
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Common Core Standard: Interpret the equation y = mx + b as defining a linear function, whose graph is a straight
line.
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Slope is the steepness of a line
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It is the rise of the line divided by how much over the line goes
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Often called rise over run
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Slope is often shown as a fraction, which is actually helpful!
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There are four types of slope
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Positive, negative, zero, and undefined
Positive slope
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In the equation, the m or slope will be positive
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The graph of the line goes into the first quadrant, in which both x and y are positive
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The line goes from left to right
Negative slope
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In the equation, the m or slope will be negative
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The graph of the line goes into the 2nd and 4th quadrants, which both have a negative coordinates
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The line goes from right to left
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In the equation, the m or slope will be zero
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The graph is a horizontal line
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This is also called no slope
Zero slope
Undefined slope
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In the equation, the m or slope will have a zero in the denominator
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The graph is a vertical line
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This is also called no solution
How to graph using slope-intercept form or y = mx + b
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Begin at the y-intercept or b, put the first point for the line there
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Then starting at the y-intercept, follow the slope, the numerator is how many you should go up or down (up
if positive, down is negative), the denominator is how many you should go over to the right
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Put a point there, then continue following the slope
Ex: Graph of y = -2x + -3
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The y-intercept is -3
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The rate of change is -2 or
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This means, start at y = -3, then follow the rate of change, down 2 (because it’s negative) then over 1
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Example: y = 3x + 5
o The y-intercept is 5
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, which means it is a negative slope
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The slope or rate of change is 3, which is positive
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This means start at y= 5, then go up 3 over 1, as the slope is 3 or as a fraction
Example y = 0x + 5
o This line has a zero slope
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This means that the line is horizontal
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The equation could also be written as y = 5
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Begin by placing a point at y =5
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Then draw a horizontal line through the point
Example: y = 4/0x -2
o This line has an undefined slope
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This means that the line is vertical
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Put a point at x = -2