3-4 equations of lines
DESCRIPTION
3-4 Equations of Lines. You found the slopes of lines. Write an equation of a line given information about the graph. Solve problems by writing equations. Writing an Equation of a Line. Slope-intercept form Given the slope m and the y-intercept b, y = mx + b Point-slope form - PowerPoint PPT PresentationTRANSCRIPT
3-4 Equations of Lines
You found the slopes of lines.
• Write an equation of a line given information about the graph.
• Solve problems by writing equations.
Writing an Equation of a LineSlope-intercept form
Given the slope m and the y-intercept b, y = mx + bPoint-slope formGiven the slope m and a point (x1,y1)y − y1 = m(x−x1)Two pointsGiven two points (x1,y1) and (x2,y2)
12
12
xx
yym
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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.
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.
Slope and a Point on the Line
Point-slope form
Write an equation in point-slope form of the line
whose slope is that contains (–10, 8). Then
graph the line.
Simplify.
Graph the given point (–10, 8).
Use the slope
to find another point 3 units down and 5 units to the right.
Draw a line through these two points.
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
x1 = 4, x2 = –2, y1 = 9, y2 = 0
Simplify.
Step 2 Now use the point-slope form and either point to write an equation.
Distributive Property
Add 9 to each side.
Answer:
Point-slope form
Using (4, 9):
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
x1 = –3, x2 = –1, y1 = –7, y2 = 3
Simplify.
Step 2 Now use the point-slope form and either point to write an equation.
Distributive Property
Answer:
m = 5, (x1, y1) = (–1, 3)
Point-slope form
Using (–1, 3):
Add 3 to each side.y = 5x + 8
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
Point-Slope form
m = 0, (x1, y1) = (5, –2)
Step 2
Answer:
Simplify.Subtract 2 from each side.y = –2
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Parallel lines that are not vertical have equal slopes.
Two non-vertical lines are perpendicular if the product of their slope is -1.
Vertical and horizontal lines are always perpendicular to one another.
Write Equations of Parallel or Perpendicular 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.
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 + 750m = 525, b = 750Answer: The total annual cost can be represented
by the equation A = 525r + 750.
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?
Answer: The first complex offers the better rate: one year costs $7050 instead of $7400.
3-4 Assignment
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