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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