Download presentation

1
**LINEAR EQUATIONS MSJC ~ Menifee Valley Campus**

Math Center Workshop Series Janice Levasseur

2
Equations of the Line Write the equation of a line given the slope and the y-intercept Write the equation of a line given the slope and a point Write the equation of a line given two points

3
Equations of the Line Write the equation of a line given the slope and the y-intercept: m and (0, b) Write the equation of a line given the slope and a point Write the equation of a line given two points

4
**Ex: Find an equation of the line with slope = 6 and y-int = (0, -3/2)**

Recall: slope-intercept form of a linear equation y = mx + b, where m and b are constants Given the y-int = (0, -3/2) b = - 3/2 Given the slope = 6 m = 6 Putting everything together we get the equation of the line in slope-int form: y m 6 x + - 3/2 b = y = 6x – 3/2

5
**Ex: Find an equation of the line with slope = 1. 23 and y-int = (0, 0**

Recall: slope-intercept form of a linear equation y = mx + b, where m and b are constants Given the y-int = (0, 0.63) b = 0.63 Given the slope = 1.23 m = 1.23 Putting everything together we get the equation of the line in slope-int form: y m + b = 1.23 x 0.63 y = 1.23x

6
Equations of the Line Write the equation of a line given the slope and the y-intercept Write the equation of a line given the slope and a point: m and (x1, y1) Write the equation of a line given two points

7
**Ex: Find an equation of the line with slope = -3 that contains the point (4, 2)**

Start with the slope-intercept form of a linear equation y = mx + b Slope = - 3 y = - 3x + b What is b, though? What is b, though? Use the given point (4, 2) x = 4 and y = 2 y = - 3x + b 2 = - 3(4) + b put it together 2 = b we have m and b 14 = b y = - 3 x + 14

8
**Ex: Find an equation of the line with slope = -0**

Ex: Find an equation of the line with slope = that contains the point (2, -6) Start with the slope-intercept form of a linear equation y = mx + b Slope = y = x + b What is b, though? Use the given point (2, -6) x = 2 and y = -6 y = x + b -6 = -0.25(2) + b put it together -6 = b we have m and b -5.5 = b y = -0.25x – 5.5

9
Equations of the Line Write the equation of a line given the slope and the y-intercept Write the equation of a line given the slope and a point Write the equation of a line given two points: (x1, y1) and (x2, y2)

10
**Ex: Find an equation of the line containing the points (-2, 1) and (3, 5)**

First, find the slope of the line containing the points: Slope = m = rise = y1 - y2 = 1 – (5) run x1 - x – 3 Now we have m = 4/5 and two points. Pick one point and proceed like in the last section.

11
**We have m = 4/5, the point (-2, 1), and y = mx + b**

Slope = 4/5 y = 4/5x + b What is b, though? Use the given point (-2, 1) x = -2 and y = 1 y = 4/5x + b 1 = 4/5(-2) + b 1 = (-8/5) + b 13/5 = b put it together we have m and b y = 4/5x + 13/5

12
**Ex: Find an equation of the line containing the points (-4, 5) and (-2, -3)**

First, find the slope of the line containing the points: Slope = m = rise = y1 - y2 = 5 – (-3) run x1 - x – (-2) = -4 Now we have m = -4 and two points. Pick one point and proceed like in the last section.

13
**We have m = -4, the point (-4, 5), and y = mx + b**

Slope = -4 y = -4x + b What is b, though? Use the given point (-4, 5) x = -4 and y = 5 y = -4x + b 5 = -4(-4) + b 5 = 16 + b -11 = b put it together we have m and b y = -4x – 11

14
**Ex: Find an equation of the line containing the points (0, 0) and (1, -5)**

First, find the slope of the line containing the points: Slope = m = rise = y1 - y2 = 0 – (-5) run x1 - x – (1) = -5 Now we have m = -5 and two points. Pick one point and proceed like in the last section.

15
**We have m = -5, the point (0, 0), and y = mx + b**

Slope = -5 y = -5x + b What is b, though? Use the given point (0, 0) x = 0 and y = 0 y = -5x + b 0 = -5(0) + b 0 = 0 + b 0 = b put it together we have m and b y = -5x + 0 y = -5x

16
Equations of the Line Write the equation of a line given the slope and the y-intercept Write the equation of a line given the slope and a point Write the equation of a line given two points

17
**Parallel & Perpendicular Lines**

When we graph a pair of linear equations, there are three possibilities: the graphs intersect at exactly one point the graphs do not intersect the graphs intersect at infinitely many points We will consider a special case of situation 1 and also situation 2.

18
**Perpendicular Lines (Situation 1)**

Perpendicular lines intersect at a right angle Notation: L1: y = m1x + b1 L2: y = m2x + b2 L1 ^ L2

19
**Nonvertical perpendicular lines have slopes that are the negative reciprocals of each other:**

m1m2 = -1 ~ or ~ m1 = - 1/m2 ~ or ~ m2 = - 1/m1 If l1 is vertical (l1: x = a) and is perpendicular to l2, then l2 is horizontal (l2: y = b) ~ and ~ vice versa

20
Ex: Determine whether or not the graphs of the equations of the lines are perpendicular: l1: x + y = 8 and l2: x – y = - 1 First, determine the slopes of each line by rewriting the equations in slope-intercept form: l1: y = - x + 8 and l2: y = x + 1 1 1 m1 = and m2 = -1 1 Since m1m2 = (-1)(1) = -1, the lines are perpendicular.

21
Ex: Determine whether or not the graphs of the equations of the lines are perpendicular: l1: -2x + 3y = -21 and l2: 2y – 3x = 16 First, determine the slopes of each line by rewriting the equations in slope-intercept form: l1: y = (2/3)x - 7 and l2: y = (3/2)x + 8 m1 = and m2 = 2/3 3/2 Since m1m2 = (2/3)(3/2) = 1 = -1 Therefore, the lines are not perpendicular!

22
**Parallel Lines (Situation 2)**

Parallel lines do not intersect Notation: L1: y = m1x + b1 L2: y = m2x + b2 L1 || L2

23
**Nonvertical parallel lines have the same slopes but different y-intercepts:**

m1 = m2 ~ and ~ b1 = b2 Horizontal Parallel Lines have equations y = p and y = q where p and q differ. Vertical Parallel Lines have equations x = p and x = q where p and q differ.

24
Ex: Determine whether or not the graphs of the equations of the lines are parallel: l1: 3x - y = -5 and l2: y – 3x = - 2 First, determine the slopes and intercepts of each line by rewriting the equations in slope-intercept form: l1: y = 3x + 5 and l2: y = 3x - 2 m1 = and m2 = 3 3 b1 = and b2 = 5 -2 Since m1 = m2 and b1 = b2 the lines are parallel.

25
Ex: Determine whether or not the graphs of the equations of the lines are parallel: l1: 4x + y = 3 and l2: x + 4y = - 4 First, determine the slopes and intercepts of each line by rewriting the equations in slope-intercept form: l1: y = -4x + 3 and l2: y = (-¼)x - 1 m1 = and m2 = -4 - ¼ Since m1 = m2 the lines are not parallel.

Similar presentations

Presentation is loading. Please wait....

OK

U1B L2 Reviewing Linear Functions

U1B L2 Reviewing Linear Functions

© 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