Splash Screen. Then/Now You wrote linear equations given either one point and the slope or two points. Write equations of lines in point-slope form. Write.

You wrote linear equations given either one point and the slope or two points.

• Write equations of lines in point-slope form.

• Write linear equations in different forms.

• point-slope form

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

Simplify.

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.

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 a slope of –2.

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

Writing an Equation in Standard Form

4y – 3x = 3x – 20 – 3x

–3x + 4y = –20

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

Simplify.

Subtract 3x from each side.

3x – 4y = 20 Multiply each side by –1.

A. –2x + y = 5

B. –2x + y = 11

C. 2x – y = –11

D. 2x + y = 11

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

Writing an Equation in Slope-Intercept Form

Distributive Property

Original equation

Add 5 to each side.

Writing an Equation in Slope-Intercept Form

Simplify.

Answer: The slope-intercept form of the equation is

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

A.

B. y = –3x + 6

C. y = –3x + 3

D. y = 2x + 3

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.

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Point-Slope Form and Standard Form

Step 1 Find the slope of BC.

Slope formula

(x1, y1) = (4, 3) and

(x2, y2) = (6, –2)

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)

Point-Slope Form and Standard Form

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

Answer: 5x + 2y = 26

Original equation

Distributive Property

Add 3 to each side.

Multiply each side by 2.

Add 5x to each side.

2y = –5x + 26

5x + 2y = 26

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.

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.