Warm Up 1) Graph the line y = -3 2) You drive 60 miles in 2 hours and 150 miles in 5 hours. What is the rate of change and what does it represent?
Warm Up
1) Graph the line y = -3
2) You drive 60 miles in 2 hours and 150 miles in 5 hours. What is the rate of change and what does it represent?
Point – Slope Form
y – y1 = m(x - x1)
y – coordinate x – coordinate
Example: y – 6 = 3(x – 5)
Goes through point (5, 6) and has slope of 3
SLOPE
Point-Slope Form
(x, y)
(x1, y1) = (-2, -2)
1. Write the equation in Point-Slope Form of the graph below:
11 xxmyy
Graphing Using Point-Slope Form
2. Graph the equation 22
15 xy
Graphing Using Point-Slope Form
3. Graph the equation 23
25 xy
Write an Equation in Point-Slope Form Given a Point and a Slope
4. (-1, -3); Slope = 4
y + 3 = 4(x + 1)
5. (-10, 0); Slope = 2
y = 2(x +10)
6. (-4, 3); Slope = -6
y – 3 = -6(x +4)
11 xxmyy
Steps:
1. Find the slope between the two points.
2. Pick one point to use in order to write the equation.
3. Plug in the slope and coordinate from the point into the Point-Slope Form
Write an Equation in Point-Slope Form Given Two Points
7. (-3, 6) and (1, -2)
y – 6 = -2(x + 3) or y + 2 = -2(x – 1)
8. (-2, 3) and (-1, 1)
y – 3 = -2(x + 2) or y – 1 = -2(x + 1)
9. (-2, -5) and (7, -6)
y + 5 = - (x + 2) or y + 6 = - (x – 7)
Write an Equation in Point-Slope Form Given Two Points
9
1
11 xxmyy
9
1
Writing an Equation from a Table
What is the independent and dependent variable?
x – independent; y – dependent
Find the rate of change:
What is the slope?4/10 = 2/5
What is the relation?(-11, -7), (-1, -3), (4, -1), (19,
5) What is a possible equation in
Point-Slope Form?y + 7 = 2/5 (x + 11)
tindependenin change
dependentin change change of rate
Example:
Altitude Temp.
8000 197.6
4500 203.9
3000 206.6
2500 207.5
Boiling Point of Water
Is the relationship shown by the data in the table linear? If so, model the data with an equation.
Step 1: Find the rates of change for each ordered pair.
Step 2: Use the slope and a point to write an equation.
Ex Identify the form of each equation. Change into the stated form.
1) y = -½x + 3
2) 2x – 3y = 6
3) y – 1 = - (x + 6)
Standard
Slope-intercept
Slope-intercept &
Standard
SummarySlope - Int.
FormStandard Form Point - Slope Form
y = mx + b Ax + By = C y – y1 = m(x - x1)
x and y are variables
x and y are variables
x and y are variables
m = slopeb = y-int.
A, B and C are WHOLE Integers
(x1 y1) is a point of the equation or
graph
Wrap Up
Point-Slope Form Graph Using Point-Slope form
Start at the point Graph the slope
Write equation in point-slope form Given a point and a slope Given two points
Writing an equation from a table Find the rate of change (slope) Pick a point to plug in
What two things are given to you in the point-slope form?
11 xxmyy