1. Objectives
Graph a line and write a linear equation using point-slope form.
Write a linear equation given two points.

2. Example 1A: Using Slope and a Point to Graph
Graph the line with the given slope that contains the given point.
slope = 2; (3, 1)
Step 1 Plot (3, 1). 1
Step 2 Use the slope to move from (3, 1) to another point. • 2 •
(3, 1)
Move 2 units up and 1 unit right and plot another point.
Step 3 Draw the line connecting the two points.

3. Example 1B: Using Slope and a Point to Graph
Graph the line with the given slope that contains the given point.
slope = ; (–2, 4)
(2, 7) 4
Step 1 Plot (–2, 4). • 3
(–2, 4) •
Step 2 Use the slope to move from (–2, 4) to another point.
Move 3 units up and 4 units right and plot another point.
Step 3 Draw the line connecting the two points.

5. Example 2: Writing Linear Equations in Point-Slope Form
Write an equation in point-slope form for the line with the given slope that contains the given point. A. B. C.

6. Check It Out! Example 2
Write an equation in point-slope form for the line with the given slope that contains the given point. a.
b. slope = 0; (3, –4)
y – (–4) = 0(x – 3)
y + 4 = 0(x – 3)

7. Example 3: Writing Linear Equations in Slope-Intercept Form
Write an equation in slope-intercept form for the line with slope 3 that contains (–1, 4).
Step 1 Write the equation in point-slope form:
y – y1 = m(x – x1)
y – 4 = 3[x – (–1)]
Step 2 Write the equation in slope-intercept form by solving for y.
Rewrite subtraction of negative numbers as addition.
y – 4 = 3(x + 1)
y – 4 = 3x + 3
Distribute 3 on the right side.
Add 4 to both sides.
y = 3x + 7

8. Example 3b: Writing Linear Equations in Slope-Intercept Form
Write an equation in slope-intercept form for the line with slope -½ that contains (6, -2).
Step 1 Write the equation in point-slope form:
y – y1 = m(x – x1)
y – (-2) = -½[x – (6)]
Step 2 Write the equation in slope-intercept form by solving for y.
y + 2 = -½(x - 6)
y + 2 = -½x + 3
Distribute -½ on the right side.
Subtract 2 from both sides.
y = -½x + 1

9. Example 4A: Using Two Points to Write an Equation
Write an equation in slope-intercept form for the line through the two points.
(2, –3) and (4, 1)
Step 1 Find the slope.
Step 2 Substitute the slope and one of the points into the point-slope form.
y – y1 = m(x – x1)
y – (–3) = 2(x – 2)
Choose (2, –3).

10. Example 4A Continued
Write an equation in slope-intercept form for the line through the two points.
(2, –3) and (4, 1)
Step 3 Write the equation in slope-intercept form.
y + 3 = 2(x – 2)
y + 3 = 2x – 4
– –3
y = 2x – 7

11. Example 4B: Using Two Points to Write an Equation
Write an equation in slope-intercept form for the line through the two points.
(0, 1) and (–2, 9)
Step 1 Find the slope.
Step 2 Substitute the slope and one of the points into the point-slope form.
y – y1 = m(x – x1)
y – 1 = –4(x – 0)
Choose (0, 1).

12. Example 4B Continued
Write an equation in slope-intercept form for the line through the two points.
(0, 1) and (–2, 9)
Step 3 Write the equation in slope-intercept form.
y – 1 = –4(x – 0)
y – 1 = –4x
y = –4x + 1