Slopes: Positive, Negative, Zero and Undefined

Slopes: Positive, Negative, Zero and Undefined

Positive Slope

• Facing the graph, the line rises from left to right

• Bottom left of graph is in quadrant III, top right is in quadrant I

• Q3 (-,-) to Q1 (+, +)

• Positive slopes indicate a rising or increasing rate of change

Positive Slope

• difference in y is negative and difference in x is negative --> (-)/(-) = + , down and to the left

• difference in y is positive and difference in x is positive --> (+)/(+) = +; up and to the right

• y = mx + b, m is +

Negative Slope

• difference in y is +, difference in x is - , --> (+)/(-) = (-)

• difference in y is -, difference in x is +, --> (-) /(+) = (-)

• down and to the right (-/+)

• up and to the left (+/-)

• facing the graph, the line falls from left to right

• Starts in Q2 (-, +) and ends in Q4 (+, -)

Negative Slope

• y = -x + b

• Negative slopes indicate a decreasing slope, or rate of change

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Zero Slope (Slope = 0)

• A slope of zero: y = (0)x + b; y = b

• y = b is a horizontal line, where no matter what input you give, the output always is the same thing - the "b" value (b = y-intercept)

• hOrizOntal line = slope of 0

Zero Slope

• Horizon is the place where the sky meets the earth

• How do we get a zero slope: a vertical line has points (x₁, 5), (x₂, 5), etc. Use the slope formula: y₂ - y₁ / x₂ - x₁. ; x₂ not equal x₁

• ( 5 - 5)/ x₂ - x₁. 0 / # = 0

Undefined Slope

• Vertical Line (straight up and down)

• Remember, this type of line would NOT pass the vertical line function test

• x = constant (no "y" in the function)

• for any value of y, x will always be the same number

• same input gives multiple outputs - not a function

Undefined Slope

• looks like x = 4, x = -5

• if the x-values are always the same, when we subtract the x-values we get zero in the denominator in the slope formula

• can NEVER have a zero in the denominator

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Slope Man - How to Remember the Slope

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Multiple Choice

Categorize the slope of the line

• Positive

• Negative

• Zero

• Undefined

Multiple Choice

Categorize the slope of the line

• Positive

• Negative

• Zero

• Undefined

Multiple Choice

What kind of slope does this line have?

• positive

• negative

• undefined

• zero

Multiple Choice

What kind of slope does this line have?

• positive

• negative

• undefined

• zero

Multiple Choice

What kind of slope does this line have?

• positive

• negative

• undefined

• zero

Multiple Choice

What kind of slope does this line have?

• positive

• negative

• undefined

• zero

Multiple Choice

Categorize the slope of the line

• Positive

• Negative

• Zero

• Undefined

Multiple Choice

Categorize the slope of the line

• Positive

• Negative

• Zero

• Undefined

Multiple Choice

Categorize the slope of the line

• Positive

• Negative

• Zero

• Undefined

Multiple Choice

Categorize the slope of the line

• Positive

• Negative

• Zero

• Undefined

Multiple Choice

Categorize the slope of the line

• Positive

• Negative

• Zero

• Undefined

Multiple Choice

Find the slope of the line.

Look at your anchor and destination points. How many units down or up, right or left, to get from one point to the

other? Up or down is the top number, right or left is the bottom number)

• -2

• 2

• -1

• 1

Multiple Choice

The slope of a VERTICAL line is ____________________.

• Zero

• undefined

• negative

• positive

Multiple Choice

The slope of a HORIZONTAL line is ____________________.  

• zero
• undefined
• positive
• negative

Multiple Choice

Graph. x = 1

• a
• b
• c
• d

Multiple Choice

What type of slope does the graph have?

• Zero

• Undefined

• Negative

• Positive

Multiple Choice

What type of slope does the graph have?

• Zero

• Undefined

• Negative

• Positive