Algebra 3

Lesson 1.3

Objectives:

SSBAT write the equation of a line given the slope and y-intercept.

SSBAT write the equation of a line given the slope and a point on the line.

SSBAT write the equation of a line given 2 points.

Standards: M11.D.3.2.2

Warm-Up 1.3

Solve each for y.

13x + 5y = 7x – 2y + 14

y = - x + 2

Writing an Equation given the Slope and Y-intercept

Substitute the slope and y-intercept into the equation y = mx + b for m and b

Write the equation of each line with the given slope and y-intercept. (y = mx + b)

1. Slope is and y-intercept is 11

m b

y = x + 11

2. Slope is -9 and y-intercept is -4

m b

y = -9x – 4

3. Slope is 0 and y-intercept is 12

m b

y = 0x + 12

y = 12

Point-Slope Form of an Equation of a Line

Used to write the equation of a line given

1) A point on the line and the slope2) 2 points on the line

y - y1 = m(x - x1)

Where m is the slope and (x1 , y1) is a point on the line.

Writing the equation given the slope and a point on the line

1. Substitute the slope in for m and the point in for x1 and y1 into y – y1 = m(x – x1)

2. Put the equation in the correct form (slope-intercept or standard form given in directions)

Examples: Write an equation with the given point and slope.Write your answer in slope-intercept form.

1. Slope is 5 and through (4, -2)

m x1 y1

y – -2 = 5(x – 4)

y + 2 = 5x – 20

y = 5x – 22

y – y1 = m(x – x1)

2. Slope is ½ and through (-8, 1) m x1 y1

y – 1 = ½(x - -8)

y – 1 = ½ (x + 8)

y – 1 = ½ x + 4

y = ½ x + 5

3. Slope is and through (-1, 5)

5

2

y – 5 = (x - -1)

y – 5 = (x + 1)

5

2

5

2

0.4 5

2 5 xy

.4 5 5

2 xy

4. Slope is and through (0, 7)

4

3

y – 7 = (x – 0)

4

3

0 4

3- 7 xy

7 4

3 - xy

Writing the equation of a line given 2 points

1. Find the slope between the 2 points

m =

2. Use the slope from above and choose 1 of the given points to substitute into the point-slope equation: y – y1 = m(x – x1)

1. (8 , -1) and (2 , 5)

82

)1(5

m 6

6

1-

)8(1)1( xy

y - y1 = m(x - x1)

811 xy

71 xy

Write the equation of the line that goes through the 2 points. Write your answer in slope-intercept form.

2. Through (4, -1) and (1, 5)

41

15

m

Choose 1 of the points: (4, -1)

y – -1 = -2(x – 4)

y + 1 = -2x + 8

y = -2x + 7

3

6

2

3. Through (5, 0) and (-3, 2)

5 - 3-

0 - 2 m

4

1 -

8-

2

Choose one Point and Substitute. (5, 0)

y – 0 = -¼(x – 5)

y = -¼ x + 1.25

4. Through (-3, -4) and (6, 11)

3- -6

4- - 11 m

9

15

Choose point: (-3, -4)

)3(3

54 xy

)3(3

5 4 xy

5 3

5 4 xy

13

5 xy

3

5

Writing the Equation given the Graph

1. Find the y-intercept (b)

2. Find the Slope (m =

3 Substitute m and b into y = mx + b

Write the equation of the line represented in the graph below.

m = -

b = 3

y =

On Your Own.

1. Write the equation of the line with a slope of ¾ and a y-intercept of -1.

y = ¾ x – 1

2. Write the equation of the line with a slope of 4 and goes through the point (1, -3). Write your answer in slope-intercept form.

y = 4x – 7

Homework

Worksheet 1.3