Slope Intercept Form

Slope Intercept Form

y = mx + b

m = slope

b = y-intercept

Multiple Select

Slope is...

• the constant rate of change

• the steepness of a line

• rise/run

• change in y

  change in x

• y₂ - y₁

  x₂ - x₁

Multiple Select

The Y-Intercept is

• where a line crosses the y-axis

• the value of y when x equals zero

• the "starting point" in a situation

• the constant in an equation written in slope intercept form

• none of these

You can identify the slope and y-intercept from tables, graphs, equations, situations, points, and sequences.

**WHAT IS THE SLOPE AND Y-INTERCEPT represented in the representations above?**

Slope Intercept Form is y = mx + b

• m = slope

• The slope is always the coefficient of "x" and represents the CONSTANT RATE OF CHANGE.

• b = y-intercept

• The y-intercept is always the constant in the equation. This means it is always 'alone' or without a variabe.

Multiple Choice

What is the equation of a line with a slope of 4 and a y-intercept of 2?

• y = -4x + 2

• y = -2x + 4

• y = 4x + 2

• y = 2x + 4

Multiple Choice

What is the y-intercept in this linear equation? y= 5x - 6

• 6

• 5

• y

• -6

Multiple Choice

What is the slope in this linear equation? y= 5x - 6

• 6

• 5

• y

• -6

Calculating the Slope and Y-Intercept From Points

*Use the slope formula to calculate the slope from two points.

*Look for a point where the x value equals zero. The y-value when x equals zero is the y-intercept.

Multiple Choice

What is the slope of the line that passes through these two points (0, -2) and (3, -4)?

• 2/3

• -2/3

• 3

• -2

Multiple Choice

What is the y-intercept of the line that passes through these two points (0, -2) and (3, -4)?

• 2/3

• -2/3

• -4

• -2

Multiple Choice

What is the equation of the line that passes through these two points (0, -2) and (3, -4)?

• y = 3/2x - 2

• y = -2x -4

• y = -2/3x - 2

• y = -3/2x - 2

Calculating the Slope and Y-Intercept from a Table

*First, Calculate the slope by identifying the constant rate of change

*Then identify the point where x equals zero. The y-value in this ordered pair will be the y-intercept.

Multiple Choice

What is the slope?

• 1/2
• 2
• 7
• 3

Multiple Choice

What is the y-intercept?

• 1/2

• 2

• 7

• 3

Multiple Choice

What equation will represent this table?

• y = 1/2x + 7

• y = 2x + 7

• y = 7x + 2

• y = 1/2x + 2

Calculating the Slope and Y-Intercept From Graph

*When calculating slope from a graph it is easiest to use "rise over run."

*To identify the y-intercept, just determine where the line crosses the y-axis.

Multiple Choice

What is the slope of this line?

• -1

• 4

• 1/4

• -4

Multiple Choice

What is the y-intercept of this line?

• -1

• 4

• 3

• 0

Multiple Choice

Write the equation for the line in slope-intercept form.

• y= -1x+3

• y= 4x+3

• y=1/4x+3

• y= -4x+3

Calculating Slope and Y-Intercept from Situations

• Remember to look for key words like "each," "every," and "per" to identify your slope.

• The y-intercept is your "starting point" or what you begin with. It is only happening ONE time (given the situation).

Multiple Choice

A flower deliveryman receives $40 a day for transportation costs plus $10 for each flower delivery he makes. What is teh slope in this situation?

• 10

• 40

• -10

• -40

Multiple Choice

A flower deliveryman receives $40 a day for transportation costs plus $10 for each flower delivery he makes. What is the y-intercept in this situation?

• -10

• 10

• -40

• 40

Multiple Choice

A flower deliveryman receives $40 a day for transportation costs plus $10 for each flower delivery he makes. How many dollars (d) will he have after making x flower deliveries

• d = 10x + 40

• d = x + 10 + 40

• d = 40x + 10

• d = 10x - 40

Calculating Slope and Y-Intercept From Sequences

-To calculate the slope, we simply find the pattern and identify what is "happening."

-To calculate the y-intercept, just work backwards and use the opposite operation to identify the value of y when x equals zero.

Multiple Choice

What is the common difference or slope of this sequence?

• −16

• 84

• 16

• 0

Multiple Choice

What is the value of "y" if x equals zero (the y-intercept)?

• 68

• 84

• 16

• 100

Multiple Choice

Which equation would represent this situation?

• y = -16x + 84

• y = 16x + 84

• y = 16x + 68

• y = -16x - 68