1. Lesson 5.6 Point-Slope Form of the Equation of a Line

2. Point-Slope Form of the Equation of a Line
A line that passes through the point (x1, y1) with a slope of m.
The point-slope form of the equation of the line is:
y – y1 = m(x – x1)
There is a difference between (x1, y1) and (x, y).
(x1, y1) is a specific point on the line.
(x, y) represents ANY point on a line.

3. A line is passing through the points (-3, 6) and (1, -2)
A line is passing through the points (-3, 6) and (1, -2). Write the equation of a line in Point-Slope Form.
Step 1: Find the slope.
m = y2 -y1 = -2 – 6 = -8 = x2-x –
Step 2: Substitute one point, (-3, 6) and the slope into the Point-Slope Form equation: y – y1 = m(x – x1)
y – 6 = -2(x - -3)
y – 6 = -2(x + 3)

4. Change from Point-Slope Form to Slope-Intercept Form
Write an equation of the line that passes through (2, 3) with a slope of – ½ .
Substitute into Point-Slope Form. y – y1 = m(x – x1)
y – 3 = - ½(x – 2)
Simplify the equation to put it into slope-intercept form.
y – 3 = - ½x + 1
y = - ½x + 4

5. Which equation would you use
Which equation would you use? Slope-Intercept, Standard, or Point-Slope Form
The line passes through the points (1, 3) and (-2, 4).
Point-slope because a point is given and a slope can be determined.
The line has a slope of -4 and has a y-intercept of -12.
Slope-intercept form because a slope and the y-intercept are given.