Algebra 2

Chapter 2.4aWriting Linear Equations

Target Goals:1. Write an equation of a line in slope-intercept

form, point-slope form, or standard form given 2 points or given a point and the slope.

OPENER/REVIEW

• Find the slope of the line that passes through (4, -3) & (-4, -1)

1 3

4 4m

2

8m

1

4m

3 1

4 4m

2

8m

1

4m

1 1 1

4 4 4

Slope-Intercept Form

• The SLOPE-INTERCEPT FORM of a linear equation is y = mx + b, where the m is the slope and the b is the y-intercept.

y bmx

2 1

2 1

y ym

x x

Where the line will cross the y-axis.

Ex 1) Write the slope-intercept form of the line that passes through the 2 points from above (from the opener). 4, 3 & 4, 1

y mx b

13 4

4b

3 1 b

2 b

12

4y x

11 4

4b

1 1 b

2 b

12

4y x

Same Answer!!

Ex 2) Write the slope-intercept form of the line that passes through (5, -2) and which has a slope of -3/5.

y mx b

32 5

5b

2 3 b

1 b

31

5y x

Point-Slope Form• The POINT-SLOPE FORM, of a linear equation

is ___________________, where m is the slope, and x1 and y1 are the coordinates of a point on the line.

1 1y y m x x

1 1my xy x

2 1

2 1

y ym

x x

1 1,x y

Ex 3) Write the point-slope form of a line that passes through (2, 3) and which as a slope of ½.

1 1my xy x

13 22

y x

Ex 4) Write the point-slope form of a line that passes through (3, 2) & (-1, 4).

FIND THE SLOPE 1st!

1 1my xy x

2 1

2 1

y ym

x x

4 2

1 3m

2

4m

1

2

1

22 3y x

1

24 1y x

Either are fine and correct to have!

Standard Form

• The STANDARD FORM of a linear equation is Ax + By = C, where A, B, and C are not fractions.

• We can get to this form from either of the two other forms of linear equations!

Ex 5) Write the standard form of a line that passes through (3, 5) and has a slope of -2.

Ax By C

5 2(3) b

Starting in SLOPE-INTERCEPT form: Starting in POINT-SLOPE form:

5 6 b 11 b

2 11y x

2 11x y

5 2( 3)y x 5 2 6y x

2 5 6x y

2 11x y

Ex 6) Find the standard form of a line that passes through (0, 5) and (-2, 2).Ax By C

FIND THE SLOPE 1st!

2 1

2 1

y ym

x x

5 2

0 2m

3

2m

If you’re using slope-intercept form, use either point:

35 (0)

2b

5 b3

52

y x

3 2 10x y

2 3 10y x

3 2 10x y Either are fine and correct to have!

If you’re using point-slope form, use either point:

35 ( 0)

2y x

35

2y x

2 10 3y x

3 2 10

3 2 10

x y

x y

Either are fine and correct to have!