1. Point-Slope Form y – y1 = m(x – x1)
Derived (came from) the slope formula:
(x1, y1) = (-2, -2)
(x, y)

2. Point-Slope Form We know the point (-2, -2), so x1 = -2 and y1 = -2
Write the equation in Point-Slope Form of the graph below:
(x1, y1) = (-2, -2)
We know the point (-2, -2), so x1 = -2 and y1 = -2
(x, y)
We know the slope is 2/3
Plug it into the Point-Slope Form:

3. Example: Using Point-Slope Form to Identify Information About a Line
Use the point-slope form of each equation to identify a point the line passes through and the slope of the line.
y – 7 = 3(x – 4)
y – y1 = m(x – x1)
y – 7 = 3(x – 4)
The equation is in point-slope form.
m = 3
Read the value of m from the equation.
(x1, y1) = (4, 7)
Read the point from the equation.
The line defined by y – 7 = 3(x – 4) has slope 3, and passes through the point (4, 7).

4. Graphing Using Point-Slope Form
Graph the equation
What is the ordered pair?
(x1, y1) =
What is the slope?
m =
(2, 5)
(2, 5)

5. Graphing Using Point-Slope Form
Graph the equation
What is the ordered pair?
(x1, y1) =
What is the slope?
m =
(-2, 5)

6. Write an Equation in Point-Slope Form Given a Point and a Slope
y + 3 = 4(x + 1)
5. (-10, 0); Slope = 2
y = 2(x +10)
6. (-4, 3); Slope = -6
y – 3 = -6(x +4)

7. Write an Equation in Point-Slope Form Given Two Points
Steps:
Find the slope between the two points.
Pick one point to use in order to write the equation.
Plug in the slope and coordinate from the point into the Point-Slope Form

8. Write an Equation in Point-Slope Form Given Two Points
7. (-3, 7) and (1, -1)
y – 7 = -2(x + 3) or y + 1 = -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)

9. You can rewrite in the Slope-Intercept Form
y – 7 = ‒2(x + 3) or y + 1 = ‒2(x – 1)
y – 7 = ‒ 2x ‒ 6
y + 1 = ‒ 2x + 2
y = ‒ 2x + 1
y = ‒ 2x + 1
SAME RESULT