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.