Download presentation

Published byAngel McKinney Modified over 4 years ago

1
**Point-Slope Form 12-4 Warm Up Problem of the Day Lesson Presentation**

Course 3 Warm Up Problem of the Day Lesson Presentation

2
**Point-Slope Form 12-4 Warm Up**

Course 3 12-4 Point-Slope Form Warm Up Write 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 1 3 y = x + 2

3
**Point-Slope Form 12-4 Problem of the Day**

Course 3 12-4 Point-Slope Form 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

4
Course 3 12-4 Point-Slope Form Learn to find the equation of a line given one point and the slope.

5
**Insert Lesson Title Here**

Course 3 12-4 Point-Slope Form Insert Lesson Title Here Vocabulary point-slope form

6
Course 3 12-4 Point-Slope Form The point-slope form of an equation of a line with slope m passing through (x1, y1) is y – y1 = m(x – x1). Point on the line Point-slope form y – y1 = m (x – x1) (x1, y1) slope

7
Course 3 12-4 Point-Slope Form Additional Example 1A: Using Point-Slope Form to Identify Information About a Line 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) y – y1 = m(x – x1) The equation is in point-slope form. y – 7 = 3(x – 4) Read the value of m from the equation. m = 3 (x1, y1) = (4, 7) Read the point from the equation. The line defined by y – 7 = 3(x – 4) has slope 3, and passes through the point (4, 7).

8
Course 3 12-4 Point-Slope Form Additional Example 1B: Using Point-Slope Form to Identify Information About a Line 1 3 y – 1 = (x + 6) y – y1 = m(x – x1) 1 3 y – 1 = (x + 6) y – 1 = [x – (–6)] 1 3 Rewrite using subtraction instead of addition. m = 1 3 (x1, y1) = (–6, 1) The line defined by y – 1 = (x + 6) has slope , and passes through the point (–6, 1). 1 3

9
**Point-Slope Form 12-4 Check It Out: Example 1A**

Course 3 12-4 Point-Slope Form Check It Out: Example 1A 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) y – y1 = m(x – x1) The equation is in point-slope form. y – 5 = 2(x – 2) Read the value of m from the equation. m = 2 (x1, y1) = (2, 5) Read the point from the equation. The line defined by y – 5 = 2(x – 2) has slope 2, and passes through the point (2, 5).

10
**Point-Slope Form 12-4 Check It Out: Example 1B 2 3 y – 2 = (x + 3)**

Course 3 12-4 Point-Slope Form Check It Out: Example 1B 2 3 y – 2 = (x + 3) y – y1 = m(x – x1) 2 3 y – 2 = (x + 3) y – 2 = [x – (–3)] 2 3 Rewrite using subtraction instead of addition. m = 2 3 (x1, y1) = (–3, 2) The line defined by y – 2 = (x + 3) has slope , and passes through the point (–3, 2). 2 3

11
**Additional Example 2A: Writing the Point-Slope Form of an Equation**

Course 3 12-4 Point-Slope Form Additional Example 2A: Writing the Point-Slope Form of an Equation 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) y – y1 = m(x – x1) Substitute 5 for x1, –2 for y1, and 4 for m. [y – (–2)] = 4(x – 5) y + 2 = 4(x – 5) The equation of the line with slope 4 that passes through (5, –2) in point-slope form is y + 2 = 4(x – 5).

12
**Additional Example 2B: Writing the Point-Slope Form of an Equation**

Course 3 12-4 Point-Slope Form Additional Example 2B: Writing the Point-Slope Form of an Equation the line with slope –5 passing through (–3, 7) y – y1 = m(x – x1) Substitute –3 for x1, 7 for y1, and –5 for m. y – 7 = -5[x – (–3)] y – 7 = –5(x + 3) The equation of the line with slope –5 that passes through (–3, 7) in point-slope form is y – 7 = –5(x + 3).

13
**Point-Slope Form 12-4 Check It Out: Example 2A**

Course 3 12-4 Point-Slope Form Check It Out: Example 2A 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) y – y1 = m(x – x1) Substitute 2 for x1, –2 for y1, and 2 for m. [y – (–2)] = 2(x – 2) y + 2 = 2(x – 2) The equation of the line with slope 2 that passes through (2, –2) in point-slope form is y + 2 = 2(x – 2).

14
**Point-Slope Form 12-4 Check It Out: Example 2B**

Course 3 12-4 Point-Slope Form Check It Out: Example 2B the line with slope –4 passing through (–2, 5) y – y1 = m(x – x1) Substitute –2 for x1, 5 for y1, and –4 for m. y – 5 = –4[x – (–2)] y – 5 = –4(x + 2) The equation of the line with slope –4 that passes through (–2, 5) in point-slope form is y – 5 = –4(x + 2).

15
**Additional Example 3: Entertainment Application**

Course 3 12-4 Point-Slope Form Additional Example 3: Entertainment Application 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. 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). 20 30 2 3

16
**Additional Example 3 Continued**

Course 3 12-4 Point-Slope Form Additional Example 3 Continued y – y1 = m(x – x1) Substitute 0 for x1, 18 for y1, and for m. 2 3 y – 18 = (x – 0) 2 3 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. 2 3 y – 18 = (150) 2 3 y – 18 = 100 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.

17
**Point-Slope Form 12-4 Check It Out: Example 3**

Course 3 12-4 Point-Slope Form 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). 15 45 1 3

18
**Check It Out: Example 3 Continued**

Course 3 12-4 Point-Slope Form Check It Out: Example 3 Continued y – y1 = m(x – x1) Substitute 0 for x1, 15 for y1, and for m. 1 3 y – 15 = (x – 0) 1 3 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. 1 3 y – 15 = (300) 1 3 y – 15 = 100 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.

19
**Insert Lesson Title Here**

Course 3 12-4 Point-Slope Form Insert Lesson Title Here Lesson Quiz 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) (–5, –6), 2 2 5 (6, 4), – 2 5 y – 5 = 4(x – 3) y – 4 = –2(x + 2)

Similar presentations

OK

Pre-Class Warm Up Find the slope of the line that passes through each pair of points. 1. (3, 6) and (-1, 4) 2. (1, 2) and (6, 1) 3. (4, 6) and (2, -1)

Pre-Class Warm Up Find the slope of the line that passes through each pair of points. 1. (3, 6) and (-1, 4) 2. (1, 2) and (6, 1) 3. (4, 6) and (2, -1)

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google

Ppt on different layers of the earth Ppt on earth and space science Ppt on main idea and key details Ppt on blue planet earth Converter pub to ppt online reader Ppt on steve jobs biography page Ppt on magic lights Ppt on case study method Ppt on satellite orbit Ppt on challenges to democracy in pakistan