Slope, Y-intercept, and Slope Intercept Form

Slope and Y-Intercept
and
Slope-Intercept From

Finding Slope

Today we'll be exploring how to find the slope of the line.

What is Slope?

• Slope, it is referred to as the constant rate of change.

• Slope also tells us the direction of the line - if it goes up, down, or if it's horizontal or vertical.

Y-Intercept:

The y-intercept is the beginning value (intial value).

It is how much you start with.

At the beginning, at time Zero.

The y-intercept of a line is the number where the line of a linear equation crosses the y-axis

​How to identify the slope.

​The slope, or the rate of change, can be found by looking for the number that is affected by time... that changes every time. Look for key words: Per, each, every....

You started with $500 in your banking account and you deposit $30 each week.

Find the slope:

​How to identify the slope.

​The slope, or the rate of change, can be found by looking for the number that is affected by time... that changes every time. Look for key words: Per, each, every....

You started with $500 in your banking account and you deposit $30 each week.

Find the slope: 30

​How to identify y-intercept

​The y-intercept, or initial value, can be found by looking for the number that is not affected by time. You will be looking for a number that will remain the same regardless of time. The y-intercept will often have a word before it such as "initial, start, began, etc...".

.

You started with $500 in your banking account and you deposit $30 each week.

.

Find the y-intercept:

​How to identify y-intercept

​The y-intercept, or initial value, can be found by looking for the number that is not affected by time. You will be looking for a number that will remain the same regardless of time. The y-intercept will often have a word before it such as "initial, start, began, etc...".

.

You started with $500 in your banking account and you deposit $30 each week.

.

Find the y-intercept: 500

What is Slope?

• A slope is a ratio of the vertical change to the horizontal change.

• We measure the slope by the steepness of a line.

  • The bigger the slope, the steeper the line.

  • The smaller the slope, the flatter it gets. ​

Slope

There are four types of slopes.....

Multiple Choice

What is the slope?

• Positive

• Negative

• Zero

• Undefined

Multiple Choice

What is the slope?

• Positive

• Negative

• Zero

• No Slope

Y-Intercept

Y-Intercept:

The y-intercept is the beginning value (intial value).

It is how much you start with.

At the beginning, at time Zero.

The y-intercept of a line is the number where the line of a linear equation crosses the y-axis

You can write your answer as a coordinate point:
(x,y)

OR
y-int:

​​What is the y-intercept?

You can write your answer as a coordinate point:
(0,4)
the 0 represents at the beginning... at time zero
OR
y-int: 4

​​How do you write the answer?

Hotspot

Select the hotspot you believe is the location the y-intercept.

Hotspot

Select the hotspot you believe is the location the y-intercept.

The y-intercept on a first quadrant graph is where the line starts.

​​Y-Intercept on 1st quadrant graph.

No, the answer is written the same for this graph:
coordinate point: (0, 1.8)
OR y-int: 1.8

Will the answer look different depending on the graph?

Slope-Intercept From

Multiple Choice

What does the m represent in y=mx+b ?

• slope

• y-intercept

Multiple Choice

What does the b represent in y=mx+b ?

• slope

• y-intercept

Multiple Choice

What is the slope of the equation below?

y = 3x + 1

• 3

• 1

• 2

• 4

Multiple Choice

In the equation, y=2x+6, the 6 is the...

• slope

• y-intercept

• x-axis

• y-axis

Multiple Choice

What is the y-intercept of the equation below?

y = x - 4

• 4

• -4

• 1

• 0

Multiple Choice

What is the slope of the equation below?

y = x - 4

• 4

• -4

• 1

• 0

Notice the difference in the way the next two questions are asked.

Multiple Choice

What is the coordinate of the y-intercept?

• (-2,0)

• (0,-2)

• (2,0)

• (0,2)

Multiple Choice

What is the the y-intercept?

• -2

• 0

• 4

• 2

Multiple Choice

What is the y-intercept?

What does the y-intercept represent?

• 15

  There are 15 gallons in the tank at the start of the trip.

• 15

  The car gets 15 miles to the gallon.

• 200

  There are 200 gallons in the tank at the start of the trip.

• 200

  The car gets 200 miles to the gallon.

Multiple Choice

What is the y-intercept?

What does the y-intercept represent?

• 0

  There is 0 inches of snow on the ground before the storm.

• 0

  The snow is falling 0 inches per hour.

• 1.5

  There is 1.5 inches of snow on the ground before the storm.

• 1.5

  The snow is falling 1.5 inches per hour.

Multiple Choice

Christina has a garden that started with 100 rose bushes. She plants 2 rose bushes every week.

What is the y-intercept in this problem?

• b = 2

• b = 100

• b = -2

• b = -100

Multiple Choice

Mr. Carbone's class starts with 37 A's. Every week 3 students lose their A's.

What is the y-intercept?

• b = 37

• b = 3

• b = -37

• b = -3

Match

Match the following

b = 3

b = -3

b = 0

b = -5

Puppy

• b = 3

• b = -3

• b = 0

• b = -5

• Puppy

Calculating Slope and
Y-Intercept on Calculator

Slope from a Table

Slope from a Table

Proportional Relationships

Ratios are equal

Rate of change is constant

​Enter the numbers in STAT Edit...
a=m=3
b=0... that's how you know it proportional

​Enter the numbers in STAT Edit...
a=m=3
b=4... that's how you know it NOTproportional

What is a proportional relationship?

• A proportional relationship is a relationship in which the ratio between the two quantities is equivalent for all values.

• The table to the right represents a proportional relationship...

Constant of Proportionality

• All proportional relationships have constant ratio, which is called the unit rate.

• ​​In the table to the right, the unit rate can be found by dividing the distance by the time.

Is this proportional?

To solve, check each ordered pair for a rate of change.
10/1 = 10
20/2 = 10
70/7 = 10
100/10 = 10
Yes, the rates are constant, so this is proportional.

Is this proportional

Check all the rates of change.

-10/70 = -1/7

-9/63 = -1/7

-5/35 = -1/7

-3/21 = -1/7

All of the rates of change are constant (-1/7), so this is proportional. 

​When calculating slope:

Fill in the Blanks

What is the slope? Be sure to simplify if possible. 

Fill in the Blanks

What is the slope? Be sure to simplify if possible.

Proportional vs. Non-Proportional from a Graph

We identify the "m" term to be our slope or rise over run, while the "b" term represents the intersection of the line with the y axis

Properties of Proportional Graphs

• All graphs of proportional relationships are represented with a straight line to show a constant rate also known as LINEAR.

• All proportional relationships pass through the origin.

• Can be used to calculate the unit rate or constant of proportionality.

Proportional Relationship

Straight line

Goes through (0,0)

Not Proportional

This has a straight line but it does NOT go through the point (0,0)

You know equations are poroportional when...

• The y-intercept is 0. This means that it is on the origin!

Multiple Choice

Is the scenario proportional or non-proportional?

• Proportional

• Non-Proportional

Multiple Choice

Is the scenario proportional or non-proportional?

• Proportional

• Non-Proportional

Slope or rate of change, denoted by m, is equal to:

The Slope is always the coefficient (Next to) of the x.

The y-intercept is the constant we add or subtract. (No variable)​

​Slope Intercept Form

You find slope from graph by rising and running from one point to another.

1. Find two points on the line

2. Starting at one point, count the rise and run going to the other point

Find the slope and y-intercept given the graph

Multiple Choice

state the slope:

• $$m=\frac{4}{5}$$

• $$m=-\frac{4}{5}$$

• $$m=\frac{5}{4}$$

• $$m=-\frac{5}{4}$$

Explanation Slide...

The slope of the graph is 3/2. Slope is a measure of steepness of a line. From one point to the next is up 3 over 2... Hence, the correct choice is 3/2.

Multiple Choice

What is the slope shown on the graph?

• 2/3

• 2

• 3/2

• 3