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Chapter 5 Linear Function - Coggle Diagram
Chapter 5 Linear Function
Lesson 28
rate of change and slope
slope
vertical change/ horizontal change
rise/ run
Y2 -- Y1/ X2 -- X1
Slope = m
slope : the ratio of the vertical change to the horizontal change = the rate of change
types of slope
negative slope
m = negative #
undefine slope
x/0
vertical line
positive slope
m = positive #
0 slope
0/y
horizontal line
how to find slope
from graph
1) identify two points the line crosses through
2) Find the vertical change and the horizontal change between the 2 points
3) write values as the vertical change/ horizontal change
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from table
1) Find the difference in the y values
2) Find the difference in the x values
3) write values as the change in y/ change in x
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from set of ordered pairs
ordered pairs = ex: (3,4) (-5,8)
1) Identify one of the ordered pais as (X1,Y1) and the other as (X2, Y2)
2) Substitute values into the slope formula
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rate of change
change in the dependent variable/change in the independent variable
rate of change : rate that shows the relationship[ between two changing quantities, such as vertical and horizontal change
Lesson 29
variation
variation = changes
direct variation
y = kx
k = not 0
it must pass through (0,0)
direct variation - a relationship that can be represented by a function in the form y = kx, where k is not 0, and it must pass through (0,0)
constant of variation
k
y/x = k
Lesson 30
slope intercept form
slope intercept form
y = mx + b
m = slope; b = y- intercept
Linear equation of a nonvertical line
how to solve slope intercept form
when you have slope & y - int
slope = m; y-int = b
substitute the value of m & b into y = mx +b
when you have two points
find slope using Y2-Y1/X2-X1
substitute the value of slope, x, and y- coordinate into y = mx +b to find b
draw graph
identify two points on the line
parent function
simplest function with common characteristics
linear equation
an equation that models a linear function
y - intercept
y- coordinate where the line crosses the y- axis
linear parent function
y = x
Lesson 31
point - slope form
(y -- y1) = m (x -- x1)
y1 = y- coordinate; x1 = x-- coordinate; m = slope
(X1, Y1) represents specific point
(X,Y) represents any point
the point-slope form of an equation of nonvertical line with slope m and through point (X1,Y1) is (Y -- Y1) = m (X -- X1)
Lesson 32
Standard form
x - intercept
x - coordinate where the line crosses the x - axis
standard form of a linear equation
Ax + By = C
A, B, or C do not denote as slope or intercept points
A and B both can not be 0 because C means constant
A, B, and C are real numbers
Lesson 33
Parrallel lines and Perpendicular lines
Parrallel lines
equal distance apart
never intersect
has same slope
Perpendicular lines
intersect at 90 degree
m1 * m2 = -1
Neither
it's not parallel or perpendicular
Lesson 34
scatter plots and trend lines
correlation
a mutual relationship or connection between two variables
mutual = reciprocal
types of correlation
negative correlation
no correlation
positive correlation
strong correlation
the points are close to each other
weak correlation
the points are further to each other
interpolation
is estimating a value between two know values
trend line
a line on a scatter plot, drawn near the points that shows a correlation
it's more accurate if you have more points on the line
extrapolation
predicting value outside the range of know values
predicting beyond the graph
scatter plot
a graph that relates two different sets of data by displaying them as ordered pais.
they are usually in the first quadrant of the coordinate plane