SLOPE

SLOPE

SLOPE

SLOPE

SLOPE

SLOPE

OBJECTIVESOBJECTIVES

TO UNDERSTAND WHAT POSITIVE AND TO UNDERSTAND WHAT POSITIVE AND NEGATIVE SLOPE LOOK LIKENEGATIVE SLOPE LOOK LIKE

TO UNDERSTAND WHAT ZERO AND TO UNDERSTAND WHAT ZERO AND UNDEFINED SLOPE LOOK LIKEUNDEFINED SLOPE LOOK LIKE

TO UNDERSTAND WHAT SLOPES OF 1 AND TO UNDERSTAND WHAT SLOPES OF 1 AND -1 LOOK LIKE-1 LOOK LIKE

TO UNDERSTAND WHAT SLOPES GREATER TO UNDERSTAND WHAT SLOPES GREATER AND LESS THAN 1 LOOK LIKEAND LESS THAN 1 LOOK LIKE

SLOPESLOPESometimes, on mountain roads, you’ll see signs warning cars and trucks about very steep hills.Often the sign uses a percent to show how steep (0% would be flat and 100% would be a cliff), and a picture to show whether it’s steep going up or down.

12%

5%

You can use the same idea to measure the steepness of a line.A line (like line a) that moves upward from left to right has a positive slope.A line (like line b) that moves downward from left to right has a negative slope.

a b

Positive slope

Negative slope

POSITIVE AND NEGATIVE POSITIVE AND NEGATIVE SLOPESLOPE

ZERO SLOPE AND ZERO SLOPE AND UNDEFINED SLOPEUNDEFINED SLOPE

If a line is flat from left to right or what we call horizontal, it has a slope of 0.If a line is straight up or down or what we call vertical, it has no slope, also known as an undefined slope.

Zero slope

Undefined slope

Y

X

A line with a slope of 1 will go up to the right and make angles of 45° with both axes on a square coordinate system.

A line with a slope of -1 will go up to the left and will also make angles of 45° with both axes on a square coordinate system.

Slope of 1

Slope of -1

SLOPES OF 1 AND -1SLOPES OF 1 AND -1

Y

X

Lines with a slope greater than 1 are steeper than lines with a slope of 1.Lines with a slope between 0 and 1 are less steep than lines with a slope of 1.It can be helpful to think of lines with a slope of 1 as the “middle case” between steeper and less steep.

Slope greater than 1.

Slope between 0 and 1.

SLOPES GREATER SLOPES GREATER AND LESS THAN 1AND LESS THAN 1

Question time!Question time!You will be given three lines to look at, and then answer the questions using the knowledge you have learned.

Y

X a

b

c

Which line has a NEGATIVE slope?

a

b

c

You can use the same idea to measure the steepness of a line.A line (like line a) that moves upward from left to right has a positive slope.A line (like line b) that moves downward from left to right has a negative slope.

a b

Positive slope

Negative slope

REMEMBER:REMEMBER:POSITIVE AND NEGATIVE SLOPEPOSITIVE AND NEGATIVE SLOPE

TRY AGAIN

REMEMBER:REMEMBER:ZERO SLOPE AND UNDEFINED SLOPEZERO SLOPE AND UNDEFINED SLOPE

If a line is flat from left to right or what we call horizontal, it has a slope of 0.If a line is straight up or down or what we call vertical, it has no slope, also known as an undefined slope.

Zero slope

Undefined slope

TRY AGAIN

Y

X

a

b

c

a

b

c

Which line has a slope of 1?

YOU ARE A SUPER SLOPE SLUETH! WELL DONE!

REMEMBER:REMEMBER:ZERO SLOPE AND UNDEFINED SLOPEZERO SLOPE AND UNDEFINED SLOPE

If a line is flat from left to right or what we call horizontal, it has a slope of 0.If a line is straight up or down or what we call vertical, it has no slope, also known as an undefined slope.

Zero slope

Undefined slope

TRY AGAIN

Y

X

A line with a slope of 1 will go up to the right and make angles of 45° with both axes on a square coordinate system.

A line with a slope of -1 will go up to the left and will also make angles of 45° with both axes on a square coordinate system.

Slope of 1

Slope of -1

REMEMBER:REMEMBER:SLOPES OF 1 AND -1SLOPES OF 1 AND -1

TRY AGAIN

Y

X

a

b

c

a

b

c

Which line has an UNDEFINED

slope?

SWEET SLOPE CHOICE!

You can use the same idea to measure the steepness of a line.A line (like line a) that moves upward from left to right has a positive slope.A line (like line b) that moves downward from left to right has a negative slope.

a b

Positive slope

Negative slope

REMEMBER:REMEMBER:POSITIVE AND NEGATIVE SLOPEPOSITIVE AND NEGATIVE SLOPE

TRY AGAIN

REMEMBER:REMEMBER:ZERO SLOPE AND UNDEFINED SLOPEZERO SLOPE AND UNDEFINED SLOPE

If a line is flat from left to right or what we call horizontal, it has a slope of 0.If a line is straight up or down or what we call vertical, it has no slope, also known as an undefined slope.

Zero slope

Undefined slope

TRY AGAIN

Y

X

a

b

c

a

b

c

Which line has a slope LESS

than 1?

SLOPETACULAR!

REMEMBER:REMEMBER:ZERO SLOPE AND UNDEFINED SLOPEZERO SLOPE AND UNDEFINED SLOPE

If a line is flat from left to right or what we call horizontal, it has a slope of 0.If a line is straight up or down or what we call vertical, it has no slope, also known as an undefined slope.

Zero slope

Undefined slope

TRY AGAIN

Y

X

Lines with a slope greater than 1 are steeper than lines with a slope of 1.Lines with a slope between 0 and 1 are less steep than lines with a slope of 1.It can be helpful to think of lines with a slope of 1 as the “middle case” between steeper and less steep.

Slope greater than 1.

Slope between 0 and 1.

REMEMBER:REMEMBER:SLOPES GREATER AND LESS THAN 1SLOPES GREATER AND LESS THAN 1

TRY AGAIN

Y

X

a

b

c

a

b

c

Which line has a POSITIVE

slope?

YOU ARE A SLICK SLOPESTER DUDE!

REMEMBER:REMEMBER:ZERO SLOPE AND UNDEFINED SLOPEZERO SLOPE AND UNDEFINED SLOPE

If a line is flat from left to right or what we call horizontal, it has a slope of 0.If a line is straight up or down or what we call vertical, it has no slope, also known as an undefined slope.

Zero slope

Undefined slope

TRY AGAIN

You can use the same idea to measure the steepness of a line.A line (like line a) that moves upward from left to right has a positive slope.A line (like line b) that moves downward from left to right has a negative slope.

a b

Positive slope

Negative slope

REMEMBER:REMEMBER:POSITIVE AND NEGATIVE SLOPEPOSITIVE AND NEGATIVE SLOPE

TRY AGAIN

Y

Xa

b

c

a

b

c

Which line has a slope of

ZERO?

SLOPESATIONAL!

You can use the same idea to measure the steepness of a line.A line (like line a) that moves upward from left to right has a positive slope.A line (like line b) that moves downward from left to right has a negative slope.

a b

Positive slope

Negative slope

REMEMBER:REMEMBER:POSITIVE AND NEGATIVE SLOPEPOSITIVE AND NEGATIVE SLOPE

TRY AGAIN

REMEMBER:REMEMBER:ZERO SLOPE AND UNDEFINED SLOPEZERO SLOPE AND UNDEFINED SLOPE

If a line is flat from left to right or what we call horizontal, it has a slope of 0.If a line is straight up or down or what we call vertical, it has no slope, also known as an undefined slope.

Zero slope

Undefined slope

TRY AGAIN

Y

Xa

b

c

a

b

c

Which line has a slope of -1?

STUPENDOUS SLOPE ACTION!

REMEMBER:REMEMBER:ZERO SLOPE AND UNDEFINED SLOPEZERO SLOPE AND UNDEFINED SLOPE

If a line is flat from left to right or what we call horizontal, it has a slope of 0.If a line is straight up or down or what we call vertical, it has no slope, also known as an undefined slope.

Zero slope

Undefined slope

TRY AGAIN

Y

X

A line with a slope of 1 will go up to the right and make angles of 45° with both axes on a square coordinate system.

A line with a slope of -1 will go up to the left and will also make angles of 45° with both axes on a square coordinate system.

Slope of 1

Slope of -1

REMEMBER:REMEMBER:SLOPES OF 1 AND -1SLOPES OF 1 AND -1

TRY AGAIN

Y

X

a

b

c

a

b

c

Which line has a slope GREATER

than 1?

YOU ARE A SMASHING SLOPE STUD!

You can use the same idea to measure the steepness of a line.A line (like line a) that moves upward from left to right has a positive slope.A line (like line b) that moves downward from left to right has a negative slope.

a b

Positive slope

Negative slope

REMEMBER:REMEMBER:POSITIVE AND NEGATIVE SLOPEPOSITIVE AND NEGATIVE SLOPE

TRY AGAIN

Y

X

Lines with a slope greater than 1 are steeper than lines with a slope of 1.Lines with a slope between 0 and 1 are less steep than lines with a slope of 1.It can be helpful to think of lines with a slope of 1 as the “middle case” between steeper and less steep.

Slope greater than 1.

Slope between 0 and 1.

REMEMBER:REMEMBER:SLOPES GREATER AND LESS THAN 1SLOPES GREATER AND LESS THAN 1

TRY AGAIN

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Click here to end the show.

CONGRATULATIONS YOU HAVE COMPLETED THE SUPER SLICK SLOPE STUDY

SYSTEM!You should now have a better understanding of positive and negative slope, zero slope and undefined slope, slopes of 1 and -1, and of slopes greater and less than 1.