concept 1 example 1 write and graph an equation in point-slope form (x 1, y 1 ) = (–2, 0)...

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Page 1: Concept 1 Example 1 Write and Graph an Equation in Point-Slope Form (x 1, y 1 ) = (–2, 0) Point-slope form Answer: Write the point-slope form of an equation

Cross multiply and you get:

Page 3: Concept 1 Example 1 Write and Graph an Equation in Point-Slope Form (x 1, y 1 ) = (–2, 0) Point-slope form Answer: Write the point-slope form of an equation

Write and Graph an Equation in Point-Slope Form

(x1, y1) = (–2, 0)

Point-slope form

Answer:

Write the point-slope form of an equation for a line

that passes through (–2, 0) with slope

Page 4: Concept 1 Example 1 Write and Graph an Equation in Point-Slope Form (x 1, y 1 ) = (–2, 0) Point-slope form Answer: Write the point-slope form of an equation

Write and Graph an Equation in Point-Slope Form

Answer:

Graph the equation

Plot the point at (–2, 0).

Use the slope to find another point on the line. Draw a line through the two points.

Page 5: Concept 1 Example 1 Write and Graph an Equation in Point-Slope Form (x 1, y 1 ) = (–2, 0) Point-slope form Answer: Write the point-slope form of an equation

A. A

B. B

C. C

D. D

A. y – 4 = –2(x + 3)

B. y + 3 = –2(x – 4)

C. y – 3 = –2(x – 4)

D. y + 4 = –2(x – 3)

Write the point-slope form of an equation for a line that passes through (4, –3) with slope –2.

Page 7: Concept 1 Example 1 Write and Graph an Equation in Point-Slope Form (x 1, y 1 ) = (–2, 0) Point-slope form Answer: Write the point-slope form of an equation

In standard form, the variables are on the left side of the equation. A, B, and C are all integers.

Multiply each side by 4 to eliminate the fraction.

Original equation

Distributive Property

Writing an Equation in Standard Form

Page 8: Concept 1 Example 1 Write and Graph an Equation in Point-Slope Form (x 1, y 1 ) = (–2, 0) Point-slope form Answer: Write the point-slope form of an equation

Writing an Equation in Standard Form

4y – 3x = 3x – 20 – 3x

–3x + 4y = –20

3x – 4y = 20

Answer: The standard form of the equation is 3x – 4y = 20.

Simplify.

Change the coefficient of x to be positive

Subtract 3x from each side.

Page 9: Concept 1 Example 1 Write and Graph an Equation in Point-Slope Form (x 1, y 1 ) = (–2, 0) Point-slope form Answer: Write the point-slope form of an equation

A. A

B. B

C. C

D. D

A. –2x + y = 5

B. –2x + y = 7

C. 2x - y = -11

D. 2x + y = 11

Write y – 3 = 2(x + 4) in standard form.

Page 10: Concept 1 Example 1 Write and Graph an Equation in Point-Slope Form (x 1, y 1 ) = (–2, 0) Point-slope form Answer: Write the point-slope form of an equation

Example 3

Writing an Equation in Slope-Intercept Form

Distributive Property

Original equation

Add 5 to each side.

Simplify.

Page 11: Concept 1 Example 1 Write and Graph an Equation in Point-Slope Form (x 1, y 1 ) = (–2, 0) Point-slope form Answer: Write the point-slope form of an equation

A. A

B. B

C. C

D. D

Write 3x + 2y = 6 in slope-intercept form.

A.

B. y = –3x + 6

C. y = –3x + 3

D. y = 2x + 3

Page 12: Concept 1 Example 1 Write and Graph an Equation in Point-Slope Form (x 1, y 1 ) = (–2, 0) Point-slope form Answer: Write the point-slope form of an equation

Point-Slope Form and Standard Form

A. GEOMETRY The figure shows trapezoid ABCD with bases AB and CD.

Write an equation in point-slope form for the line containing the side BC.

___

Page 13: Concept 1 Example 1 Write and Graph an Equation in Point-Slope Form (x 1, y 1 ) = (–2, 0) Point-slope form Answer: Write the point-slope form of an equation

Point-Slope Form and Standard Form

Step 1 Find the slope of BC.

Slope formula

(x1, y1) = (4, 3)

(x2, y2) = (6, –2)

Page 14: Concept 1 Example 1 Write and Graph an Equation in Point-Slope Form (x 1, y 1 ) = (–2, 0) Point-slope form Answer: Write the point-slope form of an equation

Point-Slope Form and Standard Form

Step 2 You can use either point for (x1, y1) in the point-slope form.

Using (4, 3) Using (6, –2)

y – y1 = m(x – x1) y – y1 = m(x – x1)

Page 15: Concept 1 Example 1 Write and Graph an Equation in Point-Slope Form (x 1, y 1 ) = (–2, 0) Point-slope form Answer: Write the point-slope form of an equation

Point-Slope Form and Standard Form

B. Write an equation in standard form for the same line.

Answer: 5x + 2y = 26

Original equation

Distribute Property

Add 3 to each side.

Multiply each side by 2.

Add 5x to each side.

2y = –5x + 26

5x + 2y = 26

Page 16: Concept 1 Example 1 Write and Graph an Equation in Point-Slope Form (x 1, y 1 ) = (–2, 0) Point-slope form Answer: Write the point-slope form of an equation

A. A

B. B

C. C

D. D

A. y – 6 = 1(x – 4)

B. y – 1 = 1(x – 3)

C. y + 4 = 1(x + 6)

D. y – 4 = 1(x – 6)

A. The figure shows right triangle ABC. Write the point-slope form of the line containing the hypotenuse AB.

Page 17: Concept 1 Example 1 Write and Graph an Equation in Point-Slope Form (x 1, y 1 ) = (–2, 0) Point-slope form Answer: Write the point-slope form of an equation

A. A

B. B

C. C

D. D

A. –x + y = 10

B. –x + y = 3

C. –x + y = –2

D. x – y = 2

B. The figure shows right triangle ABC. Write the equation in standard form of the line containing the hypotenuse.