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
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