1. Remember!
If you are absent, do the following BEFORE you come back to class
Go to my website (type Muehleck into Google)
Click on the lesson notes link on the day you were absent and go through the examples
Try the homework problems listed on the day you were absent
Now you won’t be behind!

2. Lesson Objectives: I will be able to …
Graph a line and write a linear equation using
point-slope form
Write a linear equation given two points
Language Objective: I will be able to …
Read, write, and listen about vocabulary, key
concepts, and examples

3. Graph the line given the slope and y-intercept.
Check It Out! Example 1a
Graph the line given the slope and y-intercept.
slope = 2, y-intercept = –3
Step 1 The y-intercept is –3, so the line contains (0, –3). Plot (0, –3).
Run = 1
Rise = 2 •
Step 2 Slope =
Count 2 units up and 1 unit right from (0, –3) and plot another point. •
Step 3 Draw the line through the two points.

4. Example 1B: Graphing by Using Slope and y-intercept
Graph the line given the slope and y-intercept.
Run = 1
slope = 4; y-intercept =
Rise = 4 •
Step 1 The y-intercept is , so the line contains (0, ). Plot (0, ). •
Step 2 Slope = Count 4 units up and 1 unit right from (0, ) and plot another point.
Step 3 Draw the line through the two points.

5. Example 2D: Writing linear Equations in Slope-Intercept Form
Write the equation that describes the line in slope-intercept form.
slope = ; y-intercept = –6
y = mx + b
Substitute the given values for m and b.
Simply if necessary.

6. Example 2B: Writing linear Equations in Slope-Intercept Form
Write the equation that describes the line in slope-intercept form.
slope = –9; y-intercept =
y = mx + b
Substitute the given values for m and b.
y = –9x +
Simply if necessary.

7. Check It Out! Example 2
A line has a slope of 8 and (3, –1) is on the line. Write the equation that describes this line in slope-intercept form.
Step 1 Find the y-intercept.
y = mx + b
Write the slope-intercept form.
–1 = 8(3) + b
Substitute 8 for m, 3 for x, and –1 for y.
–25 = b
–1 = 24 + b
–24 –24
Solve for b. Since 24 is added to b, subtract 24 from both sides to undo the addition.

8. Check It Out! Example 2 Continued
A line has a slope of 8 and (3, –1) is on the line. Write the equation that describes this line in slope-intercept form.
Step 2 Write the equation.
y = mx + b
Write the slope-intercept form.
y = 8x + (–25)
Substitute 8 for m, and –25 for b.
y = 8x – 25

9. Example 3A: Using Slope-Intercept Form to Graph
Write the equation in slope-intercept form. Then graph the line described by the equation.
y = 3x – 1
y = 3x – 1 is in the form y = mx + b
slope: m = 3 =
y-intercept: b = –1 •
Step 1 Plot (0, –1). •
Step 2 Count 3 units up and 1 unit right and plot another point.
Step 3 Draw the line connecting the two points.

10. Check It Out! Example 3b
Write the equation in slope-intercept form. Then graph the line described by the equation.
6x + 2y = 10
Step 1 Write the equation in slope intercept form by solving for y.
6x + 2y = 10
–6x –6x
2y = –6x + 10
Subtract 6x from both sides.
Since y is multiplied by 2, divide both sides by 2.

11. Check It Out! Example 3b Continued
Write the equation in slope-intercept form. Then graph the line described by the equation.
Step 2 Graph the line. •
y = –3x + 5 is in the form y = mx + b. •
slope: m =
y-intercept: b = 5
• Plot (0, 5).
• Count 3 units down and 1 unit right and plot another point.
• Draw the line connecting the two points.

12. Example 1: Using Slope and a Point to Graph
Page 25
Graph the line with slope = 2 that contains the point (3, 1).
Step 1 Plot (3, 1).
Step 2 Use the slope to move from (3, 1) to another point. 1 • 2 •
(3, 1)
Move 2 units up and 1 unit right and plot another point.
Step 3 Draw the line connecting the two points.

13. Graph the line with slope –1 that contains (2, –2).
Your Turn 1
Page 25
Graph the line with slope –1 that contains (2, –2).
Step 1 Plot (2, –2).
Step 2 Use the slope to move from (2, –2) to another point.
(2, –2)
Move 1 unit down and 1 unit right and plot another point. • −1 • 1
Step 3 Draw the line connecting the two points.

14. Page 24

15. Example 2: Writing Linear Equations in Point-Slope Form
Page 26
Write an equation in point-slope form for the line with the given slope that contains the given point. A. B. C.

16. Your Turn 2
Page 26
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)

17. Example 3: Writing Linear Equations in Slope-Intercept Form
Page 27
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)]
y – 4 = 3(x + 1)
Step 2 Write the equation in slope-intercept form by solving for y.
y – 4 = 3(x + 1)
Distribute 3 on the right side.
y – 4 = 3x + 3
y = 3x + 7

18. Step 1 Write the equation in point-slope form:
Your Turn 3
Page 27
Write an equation in slope-intercept form for the line with slope that contains (–3, 1).
Step 1 Write the equation
in point-slope form:
Step 2 Write the equation in
slope-intercept form by
solving for y.
y – y1 = m(x – x1)

19. Example 4: Using Two Points to Write an Equation
Page 28
Write an equation in slope-intercept form for the line through points (2, -3) and (4, 1).
Step 1 Find the slope.
Step 3 Write the equation in
slope-intercept form.
y + 3 = 2(x – 2)
Step 2 Substitute the slope and one of the points into the point-slope form.
y + 3 = 2x – 4
– –3
y = 2x – 7
y – y1 = m(x – x1)
y – (–3) = 2(x – 2)

20. Classwork
Assignment #25
Holt 5-7 #20, 21, 23, 24, 28, 29, 30, 36, 37