Lesson 3-4: Equations of Lines TARGETS Write an equation of a line given information about the graph. Solve problems by writing equations. Targets

Nonvertical Line Equations LESSON 3-3: Equations of Lines Nonvertical Line Equations Slope-intercept form Point-slope form y = mx + b Concept

Write an equation in slope-intercept Answer: LESSON 3-3: Equations of Lines EXAMPLE 1 Slope and y-intercept Write an equation in slope-intercept form of the line with slope of 6 and y-intercept of –3. Then graph the line. Answer: y = mx + b Slope-intercept form y = 6x + (–3) m = 6, b = –3 y = 6x – 3 Simplify. Use the slope of 6 or to find another point 6 units up and 1 unit right of the y-intercept. Plot a point at the y-intercept, –3. Draw a line through these two points. Example 1

LESSON 3-3: Equations of Lines EXAMPLE 2 Slope and a Point on the Line Write an equation in point-slope form of the line whose slope is that contains (–10, 8). Then graph the line. Point-slope form Answer: Graph the given point (–10, 8). Use the slope to find another point 3 units down and 5 units to the right. Example 2

Step 1 First find the slope of the line. LESSON 3-3: Equations of Lines EXAMPLE 3 Two Points A. Write an equation in slope-intercept form for a line containing (4, 9) and (–2, 0). Step 1 First find the slope of the line. Slope formula Step 2 Now use the point-slope form and either point to write an equation. Point-slope form Using (4, 9): Answer: Example 3

Step 1 First find the slope of the line. LESSON 3-3: Equations of Lines EXAMPLE 3 Two Points B. Write an equation in slope-intercept form for a line containing (–3, –7) and (–1, 3). Step 1 First find the slope of the line. Slope formula Step 2 Now use the point-slope form and either point to write an equation. Point-slope form Using (4, 9): Answer: Example 3

This is a horizontal line. LESSON 3-3: Equations of Lines EXAMPLE 4 Horizontal Line Write an equation of the line through (5, –2) and (0, –2) in slope-intercept form. Step 1 This is a horizontal line. Slope formula Step 2 Answer: Example 4

Horizontal & Vertical Line Equations LESSON 3-3: Equations of Lines Horizontal & Vertical Line Equations Concept

y = mx + b Slope-Intercept form 0 = –5(2) + b m = 5, (x, y) = (2, 0) LESSON 3-3: Equations of Lines EXAMPLE 5 Write Parallel or Perpendicular Equations of Lines y = mx + b Slope-Intercept form 0 = –5(2) + b m = 5, (x, y) = (2, 0) 0 = –10 + b Simplify. 10 = b Add 10 to each side. Answer: So, the equation is y = 5x + 10. Example 5

A = mr + b Slope-intercept form A = 525r + 750 m = 525, b = 750 LESSON 3-3: Equations of Lines EXAMPLE 6 Write Linear Equations RENTAL COSTS An apartment complex charges $525 per month plus a $750 annual maintenance fee. A. Write an equation to represent the total first year’s cost A for r months of rent. For each month of rent, the cost increases by $525. So the rate of change, or slope, is 525. The y-intercept is located where 0 months are rented, or $750. A = mr + b Slope-intercept form A = 525r + 750 m = 525, b = 750 Answer: The total annual cost can be represented by the equation A = 525r + 750. Example 6

Evaluate each equation for r = 12. LESSON 3-3: Equations of Lines EXAMPLE 6 Write Linear Equations RENTAL COSTS An apartment complex charges $525 per month plus a $750 annual maintenance fee. B. Compare this rental cost to a complex which charges a $200 annual maintenance fee but $600 per month for rent. If a person expects to stay in an apartment for one year, which complex offers the better rate? Evaluate each equation for r = 12. First complex: Second complex: A = 525r + 750 A = 600r + 200 = 525(12) + 750 r = 12 = 600(12) + 200 = 7050 Simplify. = 7400 Example 6

LESSON 3-3: Equations of Lines Write Linear Equations Answer: The first complex offers the better rate: one year costs $7050 instead of $7400. Example 6