Download presentation

Presentation is loading. Please wait.

Published byJeffery Shaw Modified over 6 years ago

1
**Slope-Intercept and Point-Slope Forms of a Linear Equation**

Chapter 7 Section 4 Slope-Intercept and Point-Slope Forms of a Linear Equation

2
**Learning Objective Write a linear equation in slope-intercept form**

Graph a linear equation using the slope and y-intercept Use the slope-intercept form to determine the equation of a line. Use the point-slope form to determine the equation of a line Compare the three methods of graphing linear equation. Key Vocabulary: slope, y-intercept, slope-intercept form, point-slope form

3
Slope-Intercept Form Standard form of a linear equation in two variables ax + by = c Slope-intercept form of a linear equation y = mx + b where m is the slope, and (0, b) is the y-intercept of the line To write an equation in slope-intercept form we solve for y. Graph is always a straight line with a slope of m and y-intercept of (0, b)

4
**Slope-Intercept Form Examples**

y = 3x – 4 Slope = 3, y-intercept (0, -4) Positive slope , rises from left to right y = -2x + 5 Slope = -2, y-intercept (0, 5) Negative slope, falls from left to right Slope = , y-intercept (0, ) Positive slope, rises from left to right

5
Slope-Intercept Form Example: Write the equation x + 4y = 8 in slope-intercept form. State the slope and y-intercept. Negative slope Falls from left to right Down 1 and to the right 2

6
**Perpendicular or Parallel Lines**

Two non-vertical lines with the same slope and different y-intercepts are parallel lines. Two lines whose slopes are negative reciprocals of each other are perpendicular lines.

7
**Perpendicular or Parallel Lines**

Example: Determine if the two lines are perpendicular, parallel, or neither. 3x + y = 5 2y = -6x + 9 Two lines are parallel when their slopes are the same and the y-intercepts are different. When they do not intersect.

8
**Perpendicular or Parallel Lines**

Example: Determine if the two lines are perpendicular, parallel, or neither. 5x - 4y = x + 5y = 10 To determine if two lines are perpendicular multiply the slopes of the two lines together. If the product is -1 then the slopes are negative reciprocals, and the lines are perpendicular.

9
**Graph a Linear Equation using Slope and y-intercept**

Method 1: Graph by plotting Method 2: Graph by x- and y-intercept x-intercept (x, 0) y-intercept (0, y) Method 3: Graph by Slope and y-intercept Form Solve the equation for y Determine the y-intercept point (0,b) If a positive slope we move up and to the right If a negative slope we move down and to the right

10
**Graph a Linear Equation using Slope and y-intercept**

Write 2x + 3y = 6 in slope-intercept form; then graph. (-3,4) (0,2) (0,0) (3,0) Down and to the right if negative

11
**Graph a Linear Equation using Slope and y-intercept**

Graph -2x + 5y = 10 using the slope and y-intercept. (5, 4) (0,2) (0,0) Up and to the right if positive

12
**Use the Slope-Intercept Form Determine the Equation of Line 1**

First: Take two points and use the slope formula to determine the slope Second: determine the y-intercept (0, b) from the line? y-intercept (0,-5) Third: write the formula y = mx + b b is where the line crosses the y axis y = 2x - 5 (3, 1) (0,0) (0,-5)

13
**Point-Slope Form of a Linear Equation**

When we know the slope and a point on the line we can use Point-Slope form to determine the equation y – y1 = m(x – x1) Where m is the slope of the line and (x1, y1) is a point on the line.

14
**Point-Slope Form of a Linear Equation**

Write an equation, in slope-intercept form, of a line that goes through the point (-1, 4) and has a slope of 3. m = 3 goes through points (-1, 4) y-intercept (0,7) Standard Form ax + by = c -3x + y = 7 3x – y = -7

15
**Point-Slope Form of a Linear Equation**

Write an equation, in slope-intercept form, of a line that goes through the point (8, -2) and has a slope of m = goes through points (8,-2) y-intercept (0,-8) Standard Form ax + by = c x + y = -8 Multiply by -1 x – y = 8

16
**Slope Intercept Form and Point-Slope Form**

Sometimes we may have to use both formulas to find the equation. Find an equation of the line through the points (-1, 5) and (3,-3) Write the equation in slope-intercept form. m = -2 goes through points (-1, 5) and (3, -3) y-intercept (0,3) Standard Form ax + by = c 2x + y = 3

17
**Remember Positive and negative slopes.**

Positive Slopes move up x number of units and to the right x number of units. Negative Slopes move down x number of units and to the right x number of units.

18
Remember If the linear equation does not have a constant term, the y-intercept is the origin (0, 0) y = mx Standard Form ax + by = c Slope-Intercept Form y = mx + b Point-Slope Form y – y1 = m(x – x1) Slope

19
**Remember Writing linear equations in slope-intercept form**

If you know the slope and y-intercept form start with slope-intercept form. y = mx + b If you know the slope and a point on the line start with point-slope form. y – y1 = m(x – x1) If you know two point on the line start by finding the slope then use the point-slope form. y – y1 = m(x – x1) to find the equation.

20
HOMEWORK 7.4 Page 463 – 464: #9, 11, 14, 17, 19, 39, 49, 57, 59, 63

Similar presentations

© 2022 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