Comparing Linear Equations

The graph shows a line with a ​ (a)   slope. The VALUE of the slope is ​ (b)   . The equation of the line is

y = ​ (c)   x + ​ (d)  

• positive

• 1/2

• -1

• 2

• 0

• negative

• 5

• 1

Answer explanation

Lines that go uphill from left to right have a positive slope.

Use rise over run to find the slope.

Positive slope is found by "up and to the right" or "down and to the left".

The slope of this line is ​ (a)   and the equation for the line is ​ (b)   = ​ (c)   . Every ordered pair on the line has an y-coordinate of ​ (d)  

• 0

• y

• -2

• undefined

• x

Answer explanation

Every horizontal line has a slope of 0.

Every horizontal line has an equation "y = a number".

Rise over run would be 0 over another number. When the numerator is zero, the answer will always be zero.

The slope of this line is ​ (a)   ​ and the equation for the line is ​ ​ (b)   = ​​ (c)   . Every ordered pair on the line has an x-coordinate of ​ (d)  

• undefined

• x

• 3

• 0

• y

Answer explanation

All vertical lines have equations "x = a number".

All points on the line have the same x-coordinate.

Rise over Run will always result in a number over zero which is undefined (you are not allowed to divide by zero).

Write the equation of the line.

Mathematical Equivalence

ON

Answer explanation

The line starts on the y-axis at (-5) and then goes up 4 and left 1.

Write an equation that has an undefined slope and goes through the point (3,1)

Hint: grab a board and plot the point. Then think about what the equation of a line with an undefined slope looks like.

Mathematical Equivalence

ON

Answer explanation

If you plot (3,1) and know that an undefined slope means a vertical line, if you were graphing you would draw a vertical line that goes through that point. Every x-coordinate would be 3. Therefore, x = 3.

Mathematical Equivalence

ON

Which company shows a greater rate of change?

• Water's Edge Rafts

• Ryan's Rafts

Function A is represented by the equation.

Function B is represented by the graph.

Which function has the greater rate of change?

• Function A

• Function B

• Neither. They have the same rate of change.

• There is not enough information to answer this question.

Who has the greater rate of change?

• Smith has the greater rate of change with 5/4

• Harmon has the greater rate of change with 7/2

• Smith has the greater rate of change with 4/5

• They have the same rate of change.

Who has the greater rate of change?

• Braden has the greater rate of change with 60/3

• Omar has the greater rate of change with 100

• Braden has the greatest rate of change with 60

• They both have the same rate of change