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Notes#8: Section 2.3: Graphing lines, Section 2.4: Writing equations of lines

Forms of Lines: Lines can be written in either Slope-Intercept form (y = mx + b) or

Standard Form (Ax + By = C). You need to know how to convert from one to the other.

Converting to Slope-Intercept Form

Converting to Standard Form

Goal: y = mx + b

Goal: Ax + By = C

(where m and b are integers or fractions)

(where A, B, and C are integers and

where A is positive)

• Get y alone

• Get x and y terms on the left side and

• Reduce all fractions

the constant term on the right side of

the equation

• Multiply ALL terms by the common

denominator to eliminate the fractions

• If necessary, change ALL signs so

that the x term is positive

1.) Convert to slope-intercept form:

2.) Convert to standard form:

4x – 12y = 8

2

=

−

y

x

5

3

3.) Convert to both slope-intercept form and standard form:

1

+ = −

−

a) y – 3 = -5(x + 4)

b.)

y

1

(

x

3)

2

Section 2.3: A. Graphing Lines using the slope and y-intercept:

- Get y alone so the equation is in y = mx + b form (m = _________, b = _________)

- Graph b first. This point goes on the ____ axis.

- Use slope and count rise over run to the next point(s). When you have at least three points on your

graph, connect the points with a ruler to make a straight line.

- Label your graphed line with the original equation

Most common errors:

• Graphing b on the x-axis instead of the y-axis

• Graphing the slope in the wrong direction (e.g. forgetting a negative)

1

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