1. 2.4 More About Linear Equations
I can use slope-intercept form and point-slope form to write linear functions.
Entry Task
Write each function in slope-intercept form.
1. 4x + y = 8 2. –y = 3x 3. 2y = 10 – 6x
Determine whether each line is vertical or horizontal.
y = 0
y = –4x + 8
y = –3x
y = –3x + 5 3 4
x =
vertical
horizontal

2. Identify the y-intercept. The y-intercept b is 1.
Example 1: Write the equation of the graphed line in slope-intercept form.
Step 1
Identify the y-intercept.
The y-intercept b is 1.
Step 2 Find the slope. 3 –4 4 –3
Choose any two convenient points on the line, such as (0, 1) and (4, –2). Count from (0, 1) to (4, –2) to find the rise and the run. The rise is –3 units and the run is 4 units.
Slope is = = – .
rise
run –3 4 3
Step 3
Write the equation in slope-intercept form. 3 4
y = – x + 1
m = – and b = 1. 3 4

3. Your Turn
Write the equation of the graphed line in slope-intercept form.
The equation of the line is 3 4
y = x + 3.

5. Example 2A: Finding the Slope of a Line Given Two or More Points
Find the slope of the line through (–1, 1) and (2, –5).
Let (x1, y1) be (–1, 1) and (x2, y2) be (2, –5).
Use the slope formula.
The slope of the line is –2.

6. Example 2B: Finding the Slope of a Line Given Two or More Points
Find the slope of the line. x 4 8 12 16 y 2 5 11
Choose any two points.
Let (x1, y1) be (4, 2) and (x2, y2) be (8, 5).
Use the slope formula.
The slope of the line is . 3 4

7. Because the slope of line is constant, it is possible to use any point on a line and the slope of the line to write an equation of the line in point-slope form.

8. Check It Out! Example 3a
Write the equation of the line in slope-intercept form with slope –5 through (1, 3).
Method A Point-Slope Form
y – y1 = m(x – x1)
y – (3) = –5(x – 1)
Substitute.
y – 3 = –5(x – 1)
Simplify.
Rewrite in slope-intercept form.
y – 3 = –5(x – 1)
y – 3 = –5x + 5
Distribute.
The equation of the slope is y = –5x + 8.
y = –5x + 8
Solve for y.

9. Check It Out! Example 3b
Write the equation of the line in slope-intercept form through (–2, –3) and (2, 5).
First, find the slope. Let (x1, y1) be (–2,–3) and (x2, y2) be (2, 5).
Method B Slope-Intercept Form
y = mx + b
Rewrite the equation using m and b.
5 = (2)2 + b
5 = 4 + b
y = 2x + 1
y = mx + b
1 = b
The equation of the line is y = 2x + 1.

11. Example 5A: Writing Equations of Parallel and Perpendicular Lines
Write the equation of the line in slope-intercept form.
parallel to y = 1.8x + 3 and through (5, 2)
m = 1.8
Parallel lines have equal slopes.
Use y – y1 = m(x – x1) with (x1, y1) = (5, 2).
y – 2 = 1.8(x – 5)
y – 2 = 1.8x – 9
Distributive property.
y = 1.8x – 7
Simplify.

12. Example 5B: Writing Equations of Parallel and Perpendicular Lines
Write the equation of the line in slope-intercept form.
perpendicular to and through (9, –2)
The slope of the given line is , so the slope of
the perpendicular line is the opposite reciprocal, .
Use y – y1 = m(x – x1). y + 2 is equivalent to y – (–2).
Distributive property.
Simplify.

13. Assignment # 14
Pg #12-30 x 3, 49, 60-62

14. Selling Price ($) Rent ($) 75 9 90 12 160 26 250 44
Example 4A: Entertainment Application
The table shows the rents and selling prices of properties from a game.
Selling Price ($)
Rent ($) 75 9 90 12
160 26
250 44
Express the rent as a function of the selling price.
Let x = selling price and y = rent.
Find the slope by choosing two points. Let (x1, y1) be (75, 9) and (x2, y2) be (90, 12).

15. Example 4A Continued
To find the equation for the rent function, use point-slope form.
y – y1 = m(x – x1)
Use the data in the first row of the table.
Simplify.

16. Example 4B: Entertainment Application
Graph the relationship between the selling price and the rent. How much is the rent for a property with a selling price of $230?
To find the rent for a property, use the graph or substitute its selling price of $230 into the function.
Substitute.
y = 46 – 6
y = 40
The rent for the property is $40.

17. Check It Out! Example 5a
Write the equation of the line in slope-intercept form.
parallel to y = 5x – 3 and through (1, 4)
m = 5
Parallel lines have equal slopes.
Use y – y1 = m(x – x1) with (x1, y1) = (5, 2).
y – 4 = 5(x – 1)
y – 4 = 5x – 5
Distributive property.
y = 5x – 1
Simplify.

18. Check It Out! Example 5b
Write the equation of the line in slope-intercept form.
perpendicular to and through (0, –2)
The slope of the given line is , so the slope of
the perpendicular, line is the opposite reciprocal .
Use y – y1 = m(x – x1). y + 2 is equivalent to y – (–2).
Distributive property.
Simplify.

19. Lesson Quiz: Part I
Write the equation of each line in slope-intercept form. 1.
2. parallel to y = 0.5x + 2 and through (6, 1)
3. perpendicular to and through (4, 4)
y = –2x –1
y = 0.5x – 2

20. Lesson Quiz: Part II
4. Express the catering cost as a function of the number of people. Find the cost of catering a meal for 24 people.
Number in Group
Cost ($) 4 98 7
134 15
230
f(x) = 12x + 50; $338