1. Point Slope Form

2. Table of Contents
26: Warm-Up, Guided Practice
27: How Do I Write an Equation With a Slope and Point?

3. Warm - Up
Identify the slope and y-intercept of the following linear functions: 1. f(x) = 3x – r(x) = 2 – x 3. y(x) = ½x 4. x -1 1 2
h(x) -4 -7

4. Learning Intention/Success Criteria
LI: We are learning to write equations using a point and a slope SC: I know how to -solve simple linear equations -compute the symbolic form of a linear function given its slope and point -given a slope and point in context, construct the symbolic form of a linear function -find the point-slope form of a linear equation

5. EQ: How Do I Write an Equation With a Slope and Point?
11/27/2018

6. A number which is used to indicate the steepness of a line and if the line is tilted uphill or downhill
Slope
Indicated by the letter “m”
Point
The pair of numbers giving the location on a coordinate plane.
Written in the form: (x, y)

7. The point at which the function crosses the y-axis
Y-Intercept
Slope Intercept Form
A way of writing an equation with a slope and a y-intercept
Written: f(x) = mx + b, where m is the slope and b is the y-intercept.

8. A way of writing an equation with a point and a slope.
Point – Slope Form
Written: y – y1 = m(x – x1) where m is the slope and (x1, y1) is the point.

9. y = mx + b
Example 1: Use slope-intercept form to write a linear equation
m = 3 f(-1) = 2
m: x: y: 3 -1 2
2 = (3)(-1) + b
2 = -3 + b +3 +3
_________
5 = b
y = 3x + 5

10. Guided Practice 1 Use slope-intercept form to write a linear equation.
f(x) has a slope of -4 and f(-1) = 3

11. Guided Practice 1 Use slope-intercept form to write a linear equation.
f(x) has a slope of -4 and f(-1) = 3
A] f(x) = -4x – 1 B] f(x) = -4x + 3 C] f(x) = -4x + 1 D] f(x) = -4x – 3

12. Guided Practice 1 Use slope-intercept form to write a linear equation.
f(x) has a slope of -4 and f(-1) = 3
y = mx + b
f(x) = -4x - 1
3 = (-4)(-1) + b
3 = 4 + b -4 -4
_________
-1 = b

13. Guided Practice 2 Use slope-intercept form to write a linear equation.
g(x) has a slope of ½ and goes through (2, 3)

14. Guided Practice 2 Use slope-intercept form to write a linear equation.
g(x) has a slope of ½ and goes through (2, 3)
A] g(x) = 1/2x + 2 B] g(x) = 1/2x + 3 C] g(x) = 1/2x + 1/2 D] g(x) = 1/2x + 0

15. Guided Practice 2 Use slope-intercept form to write a linear equation.
g(x) has a slope of ½ and goes through (2, 3)
y = mx + b
f(x) = 1/2 x + 2
3 = ( ½ )(2) + b
3 = 1 + b -1 -1
_________
2 = b

16. y – y1 = m(x – x1)
Example 2: Use point-slope form to write a linear equation
m = 3 pt: (1, 5)
m: x: y: 3 1 5
y – 5 = 3(x – 1)

17. Guided Practice 3 Use point-slope form to write a linear equation.
h(x) has a slope of 2/3 and goes through (0, -1)

18. Guided Practice 3 Use point-slope form to write a linear equation.
h(x) has a slope of 2/3 and goes through (0, -1)
A] y = 2/3x – 1 B] y = 2/3x C] y + 1 = 2/3x D] y – 1 = 2/3x + 0

19. Guided Practice 3 Use point-slope form to write a linear equation.
h(x) has a slope of 2/3 and goes through (0, -1)
y – y1 = m(x – x1)
y – -1 = 2/3(x – 0)
y + 1 = 2/3(x – 0)
y + 1 = 2/3(x)

20. Guided Practice 4 Use point-slope form to write a linear equation.
m = 4 and f(3) = -5

21. Guided Practice 4 Use point-slope form to write a linear equation.
m = 4 and f(3) = -5
A] y + 5 = 4(x – 3) B] y – 5 = 4(x – 3) C] y + 5 = 4(x + 3) D] y – 5 = 4(x + 3)

22. Guided Practice 4 Use point-slope form to write a linear equation.
m = 4 and f(3) = -5
y – y1 = m(x – x1)
y – -5 = 4(x – 3)
y + 5 = 4(x – 3)

23. Example 3: Go from point – slope form to slope – intercept form
y – 4 = ½ (x + 10)
y – 4 = ½x + 5
+ 4
+ 4
________________
y = ½x + 9

24. Guided Practice 5 Go from point - slope form to slope - intercept form
y – 8 = -1/4 (x + 4)

25. Guided Practice 5 Go from point - slope form to slope - intercept form
y – 8 = -1/4 (x + 4) A] y = -1/4x + 8 B] y = -1/4x + 4 C] y = -1/4x + 9 D] y = -1/4x + 7

26. Guided Practice 5 Go from point - slope form to slope - intercept form
y – 8 = -1/4 (x + 4)
y – 8 = -1/4x – 1
+ 8
+ 8
_________________
y = -1/4x + 7