4-7 pointpoint-slope form-slope form...4-7 point-slope form if you know the slope and any point on...

Holt McDougal Algebra 1

4-7 Point-Slope Form 4-7 Point-Slope Form

Holt Algebra 1

Lesson Quiz

Lesson Presentation

Warm Up



4-7 Point-Slope Form

Warm Up

Find the slope of the line containing each pair of points.

1. (0, 2) and (3, 4) 2. (–2, 8) and (4, 2)

3. (3, 3) and (12, –15)

Write the following equations in slope-intercept form.

4. y – 5 = 3(x + 2)

5. 3x + 4y + 20 = 0

–2

–1

y = 3x + 11



Graph a line and write a linear equation using point-slope form.

Write a linear equation given two points.

Objectives



If you know the slope and any point on the line, you can write an equation of the line by using the slope formula. For example, suppose a line has a slope of 3 and contains (2, 1) . Let (x, y) be any other point on the line.

Substitute into the slope formula.

Multiply both sides

by (x - 2).

Simplify.



Additional Example 1A: Writing Linear Equations in

Point-Slope Form

Write an equation in point slope form for the line with the given slope that contains the given point.

Write the point-slope form. y – y1 = m (x – x1)



Additional Example 1B: Writing Linear Equations in

Point-Slope Form


slope = –4; (0, 3)

Write the point-slope form. y – y1 = m(x – x1)

y – 3 = –4(x – 0) Substitute –4 for m, 0 for x1

and 3 for y1.

y – 3 = –4(x – 0)



Example 1C

slope = 0; (3, –4)

Write the point-slope form.

y – (–4) = 0(x – 3) Substitute 0 for m, 3 for x1 and

–4 for y1.

Rewrite subtraction of negative

numbers as addition. y + 4 = 0(x – 3)


y – y1 = m(x – x1)



Write the equation that describes each line in slope-intercept form.

Additional Example 2A: Writing Linear Equations in

Slope-Intercept Form

Slope = 3, (–1, 4) is on the line.

Step 1 Write the equation in point-slope form:

y – 4 = 3[x – (–1)]

Step 2 Write the equation in slope-intercept form by solving for y.

y – 4 = 3(x + 1)

Rewrite subtraction of negative numbers as addition.

Distribute 3 on the right side. y – 4 = 3x + 3 + 4 + 4

y = 3x + 7 Add 4 to both sides.

y – y1 = m(x – x1)



(2, –3) and (4, 1)

Step 1 Find the slope.

Step 2 Substitute the slope and one of the points into the point-slope form.

Choose (2, –3).

y – y1 = m(x – x1)

y – (–3) = 2(x – 2)

Additional Example 2B: Writing Linear Equations in

Slope-Intercept Form

Write the equation that describes the line in slope-intercept form.



Step 3 Write the equation in slope-intercept form.

y = 2x – 7

–3 –3

Additional Example 2B Continued

Write an equation in slope-intercept form for the line through the two points.

(2, –3) and (4, 1)

y + 3 = 2(x – 2)

y + 3 = 2x – 4



Example 2C

Step 1 Write the equation in point-slope form:

y – y1 = m(x – x1)

Write the equation that describes the line in slope-intercept form.



Rewrite subtraction of negative numbers as addition.

Distribute on the right side.

+1 +1


Example 2C Continued

Write an equation in slope-intercept form for

the line with slope that contains (–3, 1).

Add 1 to both sides.



Example 2D


(1, –2) and (3, 10)

Step 1 Find the slope.

Step 2 Substitute the slope and one of the points into the point-slope form.

Choose (1, –2).

y – y1 = m(x – x1)

y – (–2) = 6(x – 1)

y + 2 = 6(x – 1)



Example 2D Continued


Step 3 Write the equation in slope-intercept form.

y + 2 = 6x – 6

– 2 – 2

y = 6x – 8

(1, –2) and (3, 10)

y + 2 = 6(x – 1)

Subtract 2 from both sides.

Distribute 6 on the right side.



Example 3: Problem-Solving Application

The cost to stain a deck is a linear function of the deck’s area. The cost to stain 100, 250, 400 square feet are shown in the table. Write an equation in slope-intercept form that represents the function. Then find the cost to stain a deck whose area is 75 square feet.



Understand the Problem 1

• The answer will have two parts—an equation in slope-intercept form and the cost to stain an area of 75 square feet.

• The ordered pairs given in the table—(100, 150), (250, 337.50), (400, 525)—satisfy the equation.

Example 3 Continued



2 Make a Plan

You can use two of the ordered pairs to find the slope. Then use point-slope form to write the equation. Finally, write the equation in slope-intercept form.

Example 3 Continued



Solve 3

Step 1 Choose any two ordered pairs from the table to find the slope.

Use (100, 150)

and (400, 525).

Step 2 Substitute the slope and any ordered pair from the table into the point-slope form.

y – 150 = 1.25(x – 100) Use (100, 150).

Example 5 Continued

y – y1 = m(x – x1)




y – 150 = 1.25(x – 100)

y – 150 = 1.25x – 125 Distribute 1.25.

y = 1.25x + 25 Add 150 to both

sides.

Step 4 Find the cost to stain an area of 75 sq. ft.

y = 1.25x + 25

y = 1.25(75) + 25 = 118.75

The cost of staining 75 sq. ft. is $118.75.

Example 3 Continued

Solve 3



Look Back 4

If the equation is correct, the ordered pairs that you did not use in Step 2 will be solutions. Substitute (400, 525) and (250, 337.50) into the equation.

y = 1.25x + 25

337.50 1.25(250) + 25

337.50 312.50 + 25

337.50 337.50

Example 3 Continued

y = 1.25x + 25

525 1.25(400) + 25

525 500 + 25

525 525

y = 1.25x + 25



Lesson Quiz: Part I

Write an equation in slope-intercept form for the line with the given slope that contains the given point.

1. Slope = –1; (0, 9) y − 9 = –(x − 0)

2. Slope = ; (3, –6) y + 6 = (x – 3)

Write an equation that describes each line the slope-intercept form.

3. Slope = –2, (2, 1) is on the line

4. (0, 4) and (–7, 2) are on the line

y = –2x + 5

y = x + 4



Lesson Quiz: Part II

5. The cost to take a taxi from the airport is a linear function of the distance driven. The cost for 5, 10, and 20 miles are shown in the table. Write an equation in slope-intercept form that represents the function.

y = 1.6x + 6

4-7 pointpoint-slope form-slope form...4-7 point-slope form if you know the slope and any point on...

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