The document provides instructions and examples for writing equations of lines using different methods such as given the slope and y-intercept, from a graph, using point-slope form, with two points, and for parallel and perpendicular lines. It also covers direct variation and writing linear models to predict data trends. Students are prompted to write equations or find values using the various line equation techniques covered.

1. 2.4 Writing Equations of Lines

2. Given the Slope and Y-Intercept
• Just plug them into y = mx + b
• Example: Write the equation for the line
with slope m = 3/2 and y-intercept b = -1

3. Your Turn!
• Write the equation for the line with
m = -1/4 and b = 5

4. Given a Graph
• Find the slope and y-intercept.
• Then, plug into y = mx + b
• Example:
• Write an equation of
the line shown.

5. Your Turn!
• Write an equation of the line shown.

6. Point-Slope Form
• y – y1 = m(x – x1)
• Used when you are given:
▫ The slope and a point
▫ Two points
▫ A parallel or perpendicular line and a
point

7. Given the Slope and a Point
• Example:
• Write an equation of the line through
(2,3) with slope of -1/2.

8. Your Turn!
• Write an equation of the line through (-3,4)
with slope of 2/3.

9. Parallel and Perpendicular Lines
• For parallel lines:
▫ use the same slope
• For perpendicular lines:
▫ use the opposite reciprocal (flip it and
change the sign)
• Then use Point-Slope form

10. Example:
• Write an equation of the line that passes
through (3, 2) and is parallel to y = -3x + 2.
• Write an equation of the line that passes
through (3, 2) and is perpendicular to
y = -3x + 2.

11. Your Turn!
• Write an equation of the line that passes
through (2, -3) and is parallel to y = 2x – 3.
• Write an equation of the line that passes
through (2, -3) and is perpendicular to
y = 2x – 3.

12. Given Two Points
• Find the slope:
• Pick one of the points
• Then use point-slope form (just like with
the slope and a point)

13. Example:
• Write and equation of the line that
passes through (-2, -1) and (3, 4).

14. Your Turn!
• Write and equation of the line that
passes through (1, 5) and (4, 2).
stop

15. Direct Variation
• x and y show direct variation when y = kx
and k ≠ 0
• k is called the constant of variation
• The graph of y = kx is always a line
through the origin (0, 0).

16. Writing and Using Direct Variation
Example:
The variables x and y vary directly, and
y = 12 when x = 4.
▫ Write an equation relating x and y.
▫ Find y when x = 5.

17. Your Turn!
The variables x and y vary directly, and
y = 15 when x = 3.
▫ Write an equation relating x and y.
▫ Find y when x = 9.

18. Identifying Direct Variation
• y = kx can also be written y/x = k
• A set of data pairs (x, y) shows direct
variation if y/x is constant.

19. Example:
• Tell whether the data show direct variation.
If so, write an equation relating x and y.
14-karat Gold Chains
Length, x (inches) 16 18 20 24 30
Price, y(dollars) 288 324 360 432 540

20. Your Turn!
• Tell whether the data show direct variation.
If so, write an equation relating x and y.
Diamonds
Weight, x (carats) 0.5 0.7 1.0 1.5 2.0
Price, y (dollars) 2250 3430 6400 11,000 20,400

21. Writing Linear Models
• In 1994, Americans purchased an average of
113 meals at restaurants. By 2006, it was
131. Write a linear model for the number
of meals purchased per person annually.
Use the model to predict how many will be
purchased per person in 2016.

22. Your Turn!
• In 2001, there were 57 million cats as pets
in the U.S. By 2008, there were 61 million.
• Write a linear model for the number of
cats as pets.
• Use the model to predict the number of
cats in 2020.