Download Bell Ringer Write each phrase as a mathematical expression

August 30, 2016
Bell Ringer Write each phrase as a
mathematical expression.
1. the sum of nine and eight
2. the sum of nine and a number
3. nine increased by a number x
COPY EACH
and
SOLVE
4. fourteen decreased by a number p
5. the product of 9 and a number
6. five more than twice a number
7. three times a number decreased by 11
Thinking with Mathematical Models
Investigation 2.2: Exploring Slope
Focus: How do you write an equation for a linear function if
you are given a graph, a table, or two points?
August 30, 2016
Linear functions are often used as models
for patterns we see in data plots!
Any linear function can be expressed by an
equation in the form: y = mx +b.
Now, let's talk about what each of those letters mean!
Ponder will you....
What do you know about the table and graph
of the function with the equation y = 3x + 2?
In particular, what do the numbers 3 and 2 tell
you about the table and graph values?
Today we will write equations using y = mx + b.
August 30, 2016
y = 3x + 2
slope
The formula for any linear function is
y = mx + b.
The coefficient m tells:
1. the rate at which the values of y increase or
decrease (the rate of change);
2. the steepness and direction of the graph;
y = 3x + 2
y = -3x + 2
August 30, 2016
y = 3x + 2
y-intercept
The coefficient b tells:
1. the point at which the graph of the
function crosses the y-axis.
y = 3x + 2
y = 3x - 2
August 30, 2016
y = mx +b
The steepness of a staircase is commonly measured by comparing two numbers,
the rise and the run. The rise is the vertical change from one step to the next, and
the run is the horizontal change from one step to the next.
The steepness of the line is the ratio of rise to
run. This ratio is the slope of the line:
rise
Vertical Change
Slope = Horizontal Change = run
y = mx +b
To find the slope, use
Slope =
y intercept =
Equation:
RISE
RUN
or
y2 - y1
Slope = x - x
2
1
August 30, 2016
Steps to Write Equation
1. Find the slope using
RISE
RUN
2. Find the y-intercept
3. Write equation in form of y = mx + b.
4. Use a table to check your work.
EXAMPLE
Graph the line that passes through the points
(-1, 1) and (1, 5)
Then, use the graph to find the slope.
Write the equation and check.
SLOPE INTERCEPT EQUATION -
Slope =
y intercept =
Equation:
August 30, 2016
PRACTICE TOGETHER
Graph the line that passes through the points
(-2, -2) and (2, 0)
Then, use the graph to find the slope.
Write the equation and check.
SLOPE INTERCEPT EQUATION -
Slope =
y intercept =
Equation:
YOUR TURN
Graph the line that passes through the points
(2, 2) and (-2, -4)
Then, use the graph to find the slope.
Write the equation and check.
SLOPE INTERCEPT EQUATION -
Slope =
y intercept =
Equation:
August 30, 2016
Slope can be...
Positive
Negative
Zero
Undefined
Given any two points on a line (x1, y1) and (x2, y2)
slope =
y2 - y1
x2 - x1
Part A
pg. 36
For the functions with the graphs below, find the
slope and y - intercept. Then write the equations
for the lines in the form y = mx + b.
August 30, 2016
pg. 36
Part A
Find the slope and y - intercept. Then write the
equations for the lines in the form y = mx + b.
rise
Vertical Change
Slope = Horizontal Change = run
SLOPE INTERCEPT EQUATION -
pg. 36
Part A
Find the slope and y - intercept. Then write the
equations for the lines in the form y = mx + b.
rise
Vertical Change
Slope = Horizontal Change = run
SLOPE -
1/2 = 0.5
INTERCEPT EQUATION -
-1
y = 0.5x - 1
August 30, 2016
pg. 36
Part A
Find the slope and y - intercept. Then write the
equations for the lines in the form y = mx + b.
rise
Vertical Change
Slope = Horizontal Change = run
SLOPE INTERCEPT EQUATION -
pg. 36
Part A
Find the slope and y - intercept. Then write the
equations for the lines in the form y = mx + b.
rise
Vertical Change
Slope = Horizontal Change = run
SLOPE -
-6/4 = -1.5
INTERCEPT -
-1
EQUATION -
y = -1.5x - 1
August 30, 2016
Part B
1. Find the equations for the linear functions that give
these tables. Write them in the form y = mx +b.
2. For each table, find the unit rate of change of y
compared to x.
Part B Cont.
3. Does the line represented by this table have a
slope that is greater than or less than the equations
you found in part 1(a) and part 1(b)?
August 30, 2016
Part C
The points (4, 2) and (-1, 7) lie on a line.
1. What is the slope of a line?
2. Find two or more points that lie on this line.
Describe your method.
3. Yvonne and Jackie observed that any two points
on a line can be used to find the slope. Are they
correct? Explain.
Part D
Kevin said that the line with the equation y = 2x
passes through the points (0,0) and (1,2). He
also said the line with equation y = -3x passes
through the points (0,0) and (1,-3). In general,
lines with equations of the form y = mx always
passes through the points (0,0) and (1, m). Is
he correct? Explain.
August 30, 2016
Part E
What is the slope of the horizontal line?
What about a vertical line?