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 slopem = 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 slopem = 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