Post on 15-Dec-2020
March 22, 2021
March 22, 2021 Today we will be
1. Reviewing ROC2. Exploring slope3. Classwork
Learning ObjectiveStudents will be able to calculate the slope of a line on a graph, from two order pairs,
and from a table of values.
Find the rate of change of the following. If it is linear, write the equation of the line: x y
0 41 72 93 11
x y2 80 63 35 1
We are on a HOMEROOM bell schedule today
March 22, 2021
x y0 41 72 93 11
x y2 80 63 35 1
Find the rate of change of the following. If it is linear, write the equation of the line:
March 22, 2021
If a relationship has a linear rate of change, then the rate of change is also called the SLOPE of the function.
x 0 1 2 3 4 5y 0 5 10 15 20 25
Change in dependent variableChange in independent variable
ΔyΔx=
Rate of Change
March 22, 2021
Finding the SLOPE of a Line
(x1 , y1)
(x2 , y2) y2 y1
x2 x1Slope = = riserun
change in ychange in x
m =y2 y1x2 x1
March 22, 2021
Have you ever seen one of these signs before?
Do you know what they mean?
March 22, 2021
What a 18% grade means is that the road RISES 18 feet for every 100 feet of length
(RUN). So, 18/100 or 0.18 which is 18%.
March 22, 2021
Did you know?!?Wheelchair Ramps: Maximum slope for hand-propelled wheelchair ramps should be 1" of rise to every 12" of length (or 8.3% grade). Maximum slope for power chairs should be 1.5" rise to 12" length (or 12.5% grade).
March 22, 2021
Find the slope of the line containing the points algebraically and graphically.
(2 , 4) and (2 , 2)(3 , 1) and (1 , 3)
March 22, 2021
Find the slope of the line containing the points algebraically and graphically.
(0 , 2) and (4 , 2)(2 , 1) and (2 , 3)
March 22, 2021
March 22, 2021
Practice Time:Find the slope of the line that passes through the points.
(-4 , 2) and (2 , 6)
(5 , -1) and ( 14 , 8)
(-2 , 3) and (4 , 6)
(3 , 5) and (3 , -3)
(-3 , 2) and (6 , 2) (-5 , 2) and (-7 , 10)
March 22, 2021
March 22, 2021
March 22, 2021
March 22, 2021
Heig
ht (f
eet)
Time (seconds)
200
400
600
800
2 4 6 8
A
B
C
D
What is the rate of change at each
section of the graph?
March 22, 2021
Which order pair is a solution of 3x y = 7?A. (3 , 4) B. (1 , 4) C. (5 , 3) D. (1 , 2)
Determine whether (7 , 1) is a solution of x 2y = 5.
Determine whether (½ , 9) is a solution of y = 4x + 7.
Solution the value that makes a equation TRUE. A solution of a two variable equation is a coordinate
(x , y) that makes the equation value true.
March 22, 2021
(0 , #)
(#, 0)
xintercept: the xcoordinate of a point where a graph crosses the xaxis. (#, 0)
yintercept: the ycoordinate of a point where a graph crosses the yaxis. (0, #)
Two special SOLUTIONS of linear functions are the xintercept and the yintercept.
March 22, 2021
Find the x-intercept and y-intercept of the following function:
4x 2y = 12
March 22, 2021
Find the x-intercept and y-intercept of the following function:
3x + 6y = 30
March 22, 2021
Find the x-intercept and y-intercept of the following function:
5x y = 5
March 22, 2021
Find the x-intercept and y-intercept of the following function:
4x 5y = 10
March 22, 2021
Horizontal and Vertical Lines
The graph of y = b is a horizontal line that passes through (0 , b).
The graph of x = a is a vertical line that passes through (a , 0).
y = b x = a
March 22, 2021
y = 2x 4Find the xintercept and the yintercept
March 22, 2021
SLOPE-INTERCEPT FORMy = mx + b
y = 3x 2 y = 3 ½x y = b + mx
SLOPE = mYINTERCEPT = b
(0, b)
March 22, 2021
Identify the slope and y-intercept of the line with the given equation or Inequality
y = ½x + 4 y < 7 2x
3x 6y = 6 x + 2y ≤ 8
y > 5 + ¾x y = 4x 9
March 22, 2021
Write the equation of the line whose slope is 2 and whose y‐intercept at (0, ‐5).
A recording studio charges musicians an initial fee of $50 to record an album. Studio time cost $35 per hour. Write an equation that gives the total cost (C) of an album as a function of studio time, in hours (h).
Write the equation of the line whose slope is ‐5 and whose y‐intercept at (0, 2).
March 22, 2021
GRAPHINGEQUATIONS and INEQUALITIESusing SlopeIntercept Form
March 22, 2021
What is the equation of the line?
A. slope = 2 ; yintercept (0 , 3)
B. slope = ½ ; yintercept (0 , 6)
C. m = 6 ; b = 7
D. slope = ¾ ; yintercept (0 , 0)
March 22, 2021
To write the equation of this line, which TWO pieces of information do you need?
March 22, 2021
March 22, 2021
March 22, 2021
There are times when the
yintercept is not going to be at an
integer value. When this happens, we can still write the
equation of the line, we just have to use pointslope form
March 22, 2021
Point‐Slope Form: Given a point (h, k) and a slope m, the point-slope form of the linear equation is:
y = m(x h) + k
A single line has an INFINITE number of equations in point‐slope form.
y = ⅓(x + 7) + 1 y = ⅓(x + 4)y = ⅓(x + 1) 1 y = ⅓(x 2) 2y = ⅓(x 5) 3
March 22, 2021
Write the equation of the lines with the given information in point-slope form: y = m(x h) + k
slope: 3/2 and point: (7 , 1)
slope: 3 and point: (5 , 7)
slope: 2/3 and point: (9 , 3)
y = m(x h) + k
y = m(x h) + k
y = m(x h) + k
March 22, 2021
Write the equation of the lines with the given information in point-slope form: y = m(x h) + k
slope: 1/3 and point: (6 , 1)
slope: 6 and point: (2 , 6)
slope: 4/3 and point: (9 , 1)
March 22, 2021
What is the POINT (x , y) on the line and the SLOPE of the line?
y = 2(x + 3) 4
y = 2/3(x 1) + 5
y = 3(x + 4) + 1
y = m(x h) + k
y = m(x h) + k
y = m(x h) + k
March 22, 2021
What is the POINT (x , y) on the line and the SLOPE of the line?
y = 2/5(x 7) + 1
y = 4(x + 9) 12
y = 3/2(x + 6) + 5
y = m(x h) + k
March 22, 2021
Write the equation of the lines with the given information in point-slope form
points: (-2 , 3) and (5 , 1)
points: (-4 , 2) and (3 , 9)
3 steps to follow:1) Find the slope2) Pick a point3) Write the equation
March 22, 2021
Write the equation of the lines with the given information in point-slope form
points: (5 , -1) and (-3 , 5)
points: (5 , 2) and (7 , -4)
March 22, 2021
Write the equation of the lines with the given information in point-slope form
March 22, 2021
Write the equation of the lines with the given information in point-slope form
March 22, 2021
Place the following in SLOPEINTERCEPT FORM
Write the equation of a line that has a slope of -3 and a point (1 , -4) on the line.
March 22, 2021
Write the equation of a line that has a slope of -3 and a point (1 , -4) on the line.
Write the equation of a line that has a slope of -½ and a point (-2 , 1) on the line.
March 22, 2021
Write the equation of a line that passes through the points (2 , -7) and (0 , -5).
Sometimes we will have to find the slope first...
March 22, 2021
Write the equation of a line that passes through the points (2 , -4) and (1 , 2).
Write the equation of a line that passes through the points (1 , 2) and (3 , 4).
March 22, 2021
Write the equation of a line that represents the linear function shown in the table.
x f(x)-4 64 48 3
x f(x)-2 -161 22 8
March 22, 2021
Find the rate of change of the following. If it is linear, write the equation of the line in slopeintercept form.
x y0 41 72 93 11
x y5 112 83 35 1
March 22, 2021
Graph the two lines below on the same coordinate plane
y = ⅔x + 5
y = ⅔(x 4) + 1
Parallel Lines - two linear equations on the same coordinate plane that have the same slope and different
y-intercepts
March 22, 2021
Graph the two lines below on the same coordinate plane
y = 4x 6
y = ¼(x + 2) 1
Perpendicular Lines - two linear equations in the same plane that have negative (or opposite) reciprocal slopes.
March 22, 2021
Graph the two lines below on the same coordinate plane
y = 2(x + 1) 3
y = 2x 5
Coinciding Lines - two equations that are the exact same. For linear equations, they have the same slope and the
same y-intercept.
March 22, 2021
March 22, 2021
Given: y = 4x + 5
What is one line that is PARALLEL to the given line?
What is one line that is PERPENDICULAR to the given line?
What is the equation of the line that is PARALLEL to the given line, but passes through the origin?
What is the equation of the line that is PARALLEL to the given line, but passes through the point (-3 , 2)?
March 22, 2021
Determining the LINE OF BEST FITThe line of best fit, commonly referred to as a trend line, is a line through a scatter plot of data points that best expresses the relationship between those points.
1. Pick two point ON the line.> One should be near the
beginning of the data and one near the end of the data
> These are NOT always going to be points from the scatter plot
> You might have to estimate a point
2. Find the SLOPE between those two points.
> ROUND (when needed) to the hundredths (2 decimal places)
3. Use the slope you just found and one of the points from step 1 to write the equation of the line
> Use pointslope form to help you write it in slopeintercept form
March 22, 2021
(5 , 9)
(2 , 5)
March 22, 2021
(0.6, 10)
(6 , 2)
March 22, 2021
(0.7 , 7)
(7 , 3)
March 22, 2021
(1 , 0.6)
(5.6 , 5.4)
March 22, 2021
Place the following in order based on strength of correlation: weakest to strongestweakest strongest
March 22, 2021
Approximating and "drawing" in a trend line.
Things to think about.1) your line should approximate the slope of the date2) your line should go through the middle of the date
March 22, 2021
March 22, 2021
Standard FormStandard FormAx + By = C
A is an whole number and B & C are integers
Three steps to place an equation in STANDARD FORM1. Place in slope-intercept form2. "move x-term" using opposites (add or subtract)3. MULTIPLY by the sign of "x-term" and the denominator of the "x-term"
March 22, 2021
Writing equations in standard form...
y = 2(x + 1) 3
y = ½x + 7
Three steps to place an equation in STANDARD FORM1. Place in slope-intercept form2. "move x-term" using opposites
(add or subtract)3. MULTIPLY by the sign of
"x-term" and the denominatorof the "x-term"
March 22, 2021
y = ¼(x 4) + 7
Writing equations in standard form...
y = 3x + 5
Three steps to place an equation in STANDARD FORM1. Place in slope-intercept form2. "move x-term" using opposites
(add or subtract)3. MULTIPLY by the sign of
"x-term" and the denominatorof the "x-term"
March 22, 2021
y = ⅔x + 4
y = 2(x 1)
Writing equations in standard form...
y = 3(x + 2) 1
y = ¾x 3
March 22, 2021
March 22, 2021