5.4 point-slope form: linear parent function: is y = x or f(x) = x. parent graph: simplest function...
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5.4 Point-Slope Form:
Linear Parent Function: is y = x or f(x) = x.
Parent Graph: Simplest function of a family of functions with common characteristics.
Linear Equation: is an equation that models a linear function.
Y-intercept: The point where the graph crosses the y-axis.
GOAL:
Whenever we are given a graph we must be able to provide the equation of the function.
Point-Slope Form: The linear equation of a nonvertical line with slope m and a point (x1, y1) is:
Slope = =
y-y1 = m(x - x1)
X value of given point.
Y value of given point.
Where does - = m(-) come from:
Slope =
Slope = m
= m
= m(x)
Let be any point on the line and substitute () for ()
= m Isolate -
Definition of Slope
The variable we use for slope
Point-Slope form.
EX: Provide the equation of the line that
passes through (8, -4) and has a slope of 2/3
SOLUTION: Provide the equation of the line that
passes through (8, -4) and has a slope of 2/3
Given: slope = point: (8, -4)
m = (8, -4) = (x1, y1)
= m(x)
= (x) Substitute point
= (x)
= (x)
= x
−𝟒−𝟒= x
= x
(-)(-) = +
Distribute slope
Isolate y
Common denominator
Graph: = x
b = -9.3
Slope up 2 right 3
YOU TRY IT: Provide the equation of the line that
passes through (3, 2) and has a slope of 4/9
YOU TRY IT: (Solution) Provide the equation of the line that
passes through (3, 2) and has a slope of 4/9
Given: slope = point: (3, 2)
m = (3, 2) = (x1, y1)
= m(x)
= (x) Substitute point
= (x)
= x
+𝟐+𝟐= x
= x
Distribute slope
Isolate y
Common denominator
Graph: = x
b = = 0.66
Slope up 4 right 9
CLASSWORK:
Page 316-317
Problems: 2, 3, 5, 8, 11,
HOW TO GRAPH POINT-SLOPE FORM: We can graph this equation by looking at the given information within the equation.
EX: Graph y – 1 = (x – 2)
Use the given point and slope:
We can see from the equation that
Point (2,1)
Slope m= Two up Three right.
Graph y – 1 = (x – 2)
YOU TRY IT:Graph the following equation:
y – 4 = - (x + 3)
Use the given point and slope:
We can see from the equation that Point (-3 ,4) Opposite of what we see!
Slope m= - Down one right two.
y – 4 = - (x + 3)
CLASSWORK:
Page 316-317
Problems: 12, 13, 14, 15
USING TWO POINTS TO WRITE THE POINT-SLOPE FORM:
Provide the point-slope equation of the line that passes through (-2, -3) and (1, 4)
In order to provide the point-slope equation of the line that passes through (-2, -3) and (1, 4) we must:
1. Find the slope
m = m = m =
2. Use one of the given points (either one) = (x)Choosing: (1, 4)
Choosing: (-2, -3) = (x)
YOU TRY IT: Provide the point-slope equation of the
line that passes through (6, -2) and (-1, 3)
In order to provide the point-slope equation of the line that passes through (6, -2) and (-1, 3) we must:
1. Find the slope
m = m = m = -
2. Use one of the given points (either one) = - (x)Choosing: (6, -2)
Choosing: (-1, 3) = - (x)
CLASSWORK:
Page 316-317
Problems: 19, 20, 21,
WRITING THE POINT-SLOPE FORM FROM A TABLE:
Provide the point-slope equation shown by the following data:
Time, X(s)
Attitude, y(m)
10 64030 59070 49090 440
Use two data points to find the rate-of-change (slope): Time, X
(s)Attitude, y
(m)
10 64030 59070 49090 440
m =
m =
m = Use the equation with a point, say (70, 490)
= (x)
YOU TRY IT: Provide the point-slope equation shown
by the following data:
Time, X(h)
Water, y(gal)
2 33203 45705 70708 10,820
Use two data points to find the rate-of-change (slope):
m =
m =
m = Use the equation with a point, say (70, 490)
= (x)
Time, X(h)
Water, y(gal)
2 33203 45705 70708 10,820
VIDEOS: Graphs
https://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/point-slope-form/v/linear-equations-in-point-slope-form
https://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/point-slope-form/v/idea-behind-point-slope-form
CLASSWORK:
Page 316-317
Problems:As many as needed to master the concept