Algebra II To solve equations To solve problems by writing equations.
Targets Write an equation of a line given information about the graph. Solve problems by writing...
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• Write an equation of a line given information about the graph. • Solve problems by writing equations. esson 3-4: Equations of Lines TARGETS
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Transcript of Targets Write an equation of a line given information about the graph. Solve problems by writing...
• Write an equation of a line given information about the graph.
• Solve problems by writing equations.
Lesson 3-4: Equations of Lines
TARGETS
Nonvertical Line Equations
y = mx + b
LESSON 3-3: Equations of Lines
Slope-intercept form Point-slope form
Slope and y-intercept
Answer:
Plot a point at the y-intercept, –3.
Use the slope of 6 or to find
another point 6 units up and1 unit right of the y-intercept.
Draw a line through these two points.
LESSON 3-3: Equations of Lines
EXAMPLE 1
Write an equation in slope-intercept form of the line with slope of 6 and y-intercept of –3. Then graph the line.
y = mx + b Slope-intercept form
y = 6x + (–3) m = 6, b = –3
y = 6x – 3 Simplify.
Slope and a Point on the Line
Answer:
Graph the given point (–10, 8).
Use the slope
to find another point 3 units down and 5 units to the right.
LESSON 3-3: Equations of Lines
EXAMPLE 2
Write an equation in point-slope form of the line
whose slope is that contains (–10, 8). Then
graph the line.
Point-slope form
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
LESSON 3-3: Equations of Lines
EXAMPLE 3
Step 2 Now use the point-slope form and either point to write an equation.
Point-slope form
Using (4, 9):
Answer:
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
LESSON 3-3: Equations of Lines
EXAMPLE 3
Step 2 Now use the point-slope form and either point to write an equation.
Point-slope form
Using (4, 9):
Answer:
Horizontal Line
Write an equation of the line through (5, –2) and (0, –2) in slope-intercept form.
Slope formula
This is a horizontal line.
Step 1
LESSON 3-3: Equations of Lines
EXAMPLE 4
Step 2
Answer:
LESSON 3-3: Equations of Lines
Horizontal & Vertical Line Equations
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.
LESSON 3-3: Equations of Lines
EXAMPLE 5
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.
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.
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
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?
LESSON 3-3: Equations of Lines
EXAMPLE 6
Write Linear Equations
Answer: The first complex offers the better rate: one year costs $7050 instead of $7400.
LESSON 3-3: Equations of Lines
