1. 12.4 Point-Slope Form

2. 12.4 Point-Slope Vocabulary
Point-Slope Equation
Another form of Linear Equation
Need slope “m” and a point on the line (x1,y1)
The equation is: y – y1 = m (x – x1)

3. 12.4 Example 1
Use the Point-Slope form of each equation to identify a point that passes through and the slope of the line.
y – 9 = -2/3 (x – 21),
Since y – y1 = m (x – x1),
y – 9 = -2/3 (x – 21) equation is point-slope form
Slope m = -2/3, and Point (x1,y1) = (21,9)

4. 12.4 Example 2 Identify the slope and a point on the line.
y – 2 = 3 (x + 8)
Since y – y1 = m ( x – x1),
y – 2 = 3 (x – (-8)) equation in point-slope form
Slope m = 3, and Point (x1,y1) = (-8,2)

5. 12.4 Example 3
Write the Point-Slope form of the equation that passes through the given slope and point.
The line with slope -2 passing through (4,1).
Since y – y1 = m (x – x1)
Now put in 1 for y1, -2 for m, and 4 for x1.
y – 1 = -2 (x – 4)

6. 12.4 Example 4
Write the Point-Slope form of the equation that passes through the given slope and point.
The line with slope 5 passing through (-2,4).
Since y – y1 = m (x – x1)
Now put in 4 for y1, 5 for m, and -2 for x1.
y – 4 = 5 (x – (-2)), then simplify
y – 4 = 5 (x + 2)

7. 12.4 Example 5a
A roller coaster starts by moving up 20 feet for every 30 feet it moves forward. Before moving forward it starts at a point 18 feet above the ground. Write the Point-Slope equation, then find the height after moving 150 feet forward.
Find slope: coaster rises 20 feet as it travels 30 feet forward, so m=20/30, reduced to m=2/3.
Coaster starts at a point 18 feet up before moving 0 feet forward, so (x1,y1) is (0,18).

8. 12.4 Example 5b (continued) Since y – y1 = m (x – x1)
Now put in y1 = 18, m = 2/3, and x1 = 0.
Y – 18 = 2/3 (x – 0), then simplify
y – 18 = 2/3 x, now substitute x = 150
y – 18 = 2/3 (150), multiply
y – 18 = 100, add 18 to both sides of equation
y – = , simplify
y = 118 feet high after moving 150 forward.