Point-Slope Form8-4

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes

Point-Slope Form8-4

Math Journal (5 Min)

• Explanation of Process – Each student will be given the title of the lesson that will be taught that day. They must then, at the beginning of class, write about what they think the process of finding the solution will be before they have been taught the lesson, and at the end of class, write about what they now know is the process of finding the solution after they have been taught the lesson. Then, each student will discuss his/her answers within their group. Finally, to leave class, each student will have to give/write 1 sentence that explained the process that pertained to the lesson.

Point-Slope Form8-4

Homework Review (5 Min)

Point-Slope Form8-4

Warm UpWrite the equation of the line that passes through each pair of points in slope-intercept form.

1. (0, –3) and (2, –3)

2. (5, –3) and (5, 1)

3. (–6, 0) and (0, –2)

4. (4, 6) and (–2, 0)

y = –3

x = 5

y = x + 2

y = – x – 213

Point-Slope Form8-4

Problem of the Day

Without using equations for horizontal or vertical lines, write the equations of four lines that form a square.

Possible answer: y = x + 2, y = x – 2, y = –x + 2, y = –x – 2

Point-Slope Form8-4

Textbook Examples (I Do) (5 Min)

Point-Slope Form8-4

Learn to find the equation of a line given one point and the slope.

Point-Slope Form8-4

Vocabulary

point-slope form

Point-Slope Form8-4

Point on the line((xx11, , yy11))

Point-slope formyy – – yy11 = = mm ( (xx – – xx11))

slopeslope

The point-slope form of an equation of a line with slope m passing through (x1, y1) is y – y1 = m(x – x1).

Point-Slope Form8-4

Use the point-slope form of each equation to identify a point the line passes through and the slope of the line.

y – 7 = 3(x – 4)

Additional Example 1A: Using Point-Slope Form to Identify Information About a Line

y – y1 = m(x – x1)

y – 7 = 3(x – 4)

m = 3

(x1, y1) = (4, 7)

The line defined by y – 7 = 3(x – 4) has slope 3, and passes through the point (4, 7).

The equation is in point-slope form. Read the value of m from the equation. Read the point from the equation.

Point-Slope Form8-4

y – 1 = (x + 6)

Additional Example 1B: Using Point-Slope Form to Identify Information About a Line

y – y1 = m(x – x1)

(x1, y1) = (–6, 1)

Rewrite using subtraction instead of addition.

13

13

y – 1 = (x + 6)

y – 1 = [x – (–6)]13

m =13

The line defined by y – 1 = (x + 6) has slope , and

passes through the point (–6, 1).

13

13

Point-Slope Form8-4

Use the point-slope form of each equation to identify a point the line passes through and the slope of the line.

y – 5 = 2 (x – 2)

Check It Out: Example 1A

y – y1 = m(x – x1)

y – 5 = 2(x – 2)

m = 2

(x1, y1) = (2, 5)

The line defined by y – 5 = 2(x – 2) has slope 2, and passes through the point (2, 5).

The equation is in point-slope form. Read the value of m from the equation. Read the point from the equation.

Point-Slope Form8-4

y – 2 = (x + 3)

Check It Out: Example 1B

23

(x1, y1) = (–3, 2)

Rewrite using subtraction instead of addition.

23

y – 2 = (x + 3)

y – 2 = [x – (–3)]23

m =23

The line defined by y – 2 = (x + 3) has slope , and

passes through the point (–3, 2).

23

23

y – y1 = m(x – x1)

Point-Slope Form8-4

Write the point-slope form of the equation with the given slope that passes through the indicated point.

the line with slope 4 passing through (5, –2)

Additional Example 2A: Writing the Point-Slope Form of an Equation

y – y1 = m(x – x1)

The equation of the line with slope 4 that passes through (5, –2) in point-slope form is y + 2 = 4(x – 5).

Substitute 5 for x1, –2 for y1, and 4 for m.

[y – (–2)] = 4(x – 5)

y + 2 = 4(x – 5)

Point-Slope Form8-4

the line with slope –5 passing through (–3, 7)

Additional Example 2B: Writing the Point-Slope Form of an Equation

y – y1 = m(x – x1)

The equation of the line with slope –5 that passes through (–3, 7) in point-slope form is y – 7 = –5(x + 3).

Substitute –3 for x1, 7 for y1, and –5 for m.

y – 7 = -5[x – (–3)]

y – 7 = –5(x + 3)

Point-Slope Form8-4

Write the point-slope form of the equation with the given slope that passes through the indicated point.

the line with slope 2 passing through (2, –2)

Check It Out: Example 2A

y – y1 = m(x – x1)

The equation of the line with slope 2 that passes through (2, –2) in point-slope form is y + 2 = 2(x – 2).

Substitute 2 for x1, –2 for y1, and 2 for m.

[y – (–2)] = 2(x – 2)

y + 2 = 2(x – 2)

Point-Slope Form8-4

the line with slope –4 passing through (–2, 5)

Check It Out: Example 2B

y – y1 = m(x – x1)

The equation of the line with slope –4 that passes through (–2, 5) in point-slope form is y – 5 = –4(x + 2).

Substitute –2 for x1, 5 for y1, and –4 for m.

y – 5 = –4[x – (–2)]

y – 5 = –4(x + 2)

Point-Slope Form8-4

A roller coaster starts by ascending 20 feet for every 30 feet it moves forward. The coaster starts at a point 18 feet above the ground. Write the equation of the line that the roller coaster travels along in point-slope form, and use it to determine the height of the coaster after traveling 150 feet forward. Assume that the roller coaster travels in a straight line for the first 150 feet.

Additional Example 3: Entertainment Application

As x increases by 30, y increases by 20, so the slope

of the line is or . The line passes through the point (0, 18).

2030

23

Point-Slope Form8-4

Additional Example 3 Continued

y – y1 = m(x – x1) Substitute 0 for x1, 18 for y1,

and for m.23

The equation of the line the roller coaster travels along, in point-slope form, is y – 18 = x. Substitute 150 for x to find the value of y.

23

y – 18 = (150)23

y – 18 = 100

y – 18 = (x – 0)23

y = 118

The value of y is 118, so the roller coaster will be at a height of 118 feet after traveling 150 feet forward.

Point-Slope Form8-4

Check It Out: Example 3

A roller coaster starts by ascending 15 feet for every 45 feet it moves forward. The coaster starts at a point 15 feet above the ground. Write the equation of the line that the roller coaster travels along in point-slope form, and use it to determine the height of the coaster after traveling 300 feet forward. Assume that the roller coaster travels in a straight line for the first 300 feet.

As x increases by 45, y increases by 15, so the slope

of the line is or . The line passes through the point (0, 15).

1545

13

Point-Slope Form8-4

Check It Out: Example 3 Continued

y – y1 = m(x – x1) Substitute 0 for x1, 15 for y1,

and for m.13

The equation of the line the roller coaster travels along, in point-slope form, is y – 15 = x. Substitute 300 for x to find the value of y.

13

y – 15 = (300)13

y – 15 = 100

y – 15 = (x – 0)13

y = 115

The value of y is 115, so the roller coaster will be at a height of 115 feet after traveling 300 feet forward.

Point-Slope Form8-4

Class work Problems (We Do) (10 Min)

• Pg. 358-359 (1-9)

Point-Slope Form8-4

Point-Slope Form8-4

Point-Slope Form8-4

Point-Slope Form8-4

Small Group CW(Yall Do) (10 Min)

• Pg. 358-359 (10-28 EOE)

Point-Slope Form8-4

Point-Slope Form8-4

Point-Slope Form8-4

Point-Slope Form8-4

Point-Slope Form8-4

Point-Slope Form8-4

Point-Slope Form8-4

Point-Slope Form8-4

Homework (You Do) (10 Min)

• Pg. 358-359 (11, 13, 15, 19, 21 odd)

Point-Slope Form8-4

Math Journal (5 Min)

• Explanation of Process – Each student will be given the title of the lesson that will be taught that day. They must then, at the beginning of class, write about what they think the process of finding the solution will be before they have been taught the lesson, and at the end of class, write about what they now know is the process of finding the solution after they have been taught the lesson. Then, each student will discuss his/her answers within their group. Finally, to leave class, each student will have to give/write 1 sentence that explained the process that pertained to the lesson.

Point-Slope Form8-4

Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

Point-Slope Form8-4

Use the point-slope form of each equation to identify a point the line passes through and the slope of the line.

1. y + 6 = 2(x + 5)

2. y – 4 = – (x – 6)

Write the point-slope form of the equation with the given slope that passes through the indicated point.

3. the line with slope 4 passing through (3, 5)

4. the line with slope –2 passing through (–2, 4)

Lesson Quiz

(–5, –6), 2

y – 5 = 4(x – 3)

y – 4 = –2(x + 2)

25

(6, 4), – 25

Point-Slope Form8-4

1. Use the point-slope form of the equation y + 4 = 5(x + 6) to identify a point the line passes through and the slope of the line.

A. (–6, –4); 5 B. (–6, –4); –5

C. (6, 4); 5

D. (6, 4); –5

Lesson Quiz for Student Response Systems

Point-Slope Form8-4

2. Identify the point-slope form of the equation of the line with slope 6 passing through the point (3, 1).

A. y – 1 = –6(x – 3) B. y + 1 = –6(x + 3)

C. y – 1 = –6(x – 3)

D. y + 1 = –6(x + 3)

Lesson Quiz for Student Response Systems