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class
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Standard Form
In order to write the equation of a line in standard form, most often it is necessary to manipulate
an equation that has been written in point-slope form or slope-intercept form. In standard form,
the x and y terms should be together on the same side of the equation, the leading coefficient
should be positive and all fractions and/or decimals should be cleared from the equation.
Standard Form: Ax 1 By 5 C
A should be
positive.
C is the constant term.
No variables.
A, B, and C should all
be integers. No
fractions or decimals.
Example A
5
Write the equation y 5 x 1 2 in standard form.
6
5
y 5 x12
6
5

6( y ) 5 6  x12 
6

6 y 5 5 x112
25 x 25 x
Step 1: Multiply each side of the equation by 6 to
eliminate the fraction.
Step 2: Subtract 5x from each side of the equation.
25 x 1 6 y 5 12
21(25 x 1 6 y ) 521(12)
Step 3: Multiply each side of the equation by 21 to
make the leading coefficient, 25, positive.
5 x 2 6 y 5212
Standard Form
© 2014 College Board. All rights reserved.
1
SpringBoard Mini-Lesson, Algebra 1 Unit 2
Standard Form (continued)
Example B
Write the equation of the line passing through the points (3, 2) and (22, 21) in standard form.
m5
21 2 2
22 2 3
23
25
3
m5
5
y 2 y 1 5 m( x 2 x 1)
3
y 2 2 5 ( x 2 3)
5
3
9
y 225 x 2
5
5
3
9
5( y 2 2) 5 5  x 2 
5
5
m5
5 y 2 10 5 3x 2 9
23x
23x
23x15 y210 529
110 110
23x 1 5 y 5 1
21(23x 5 5 y ) 521(1)
3x 2 5 y 521
Step 1: Determine the slope of the line using the slope
y 2y
formula: m5 2 1 .
x 22x 1
Step 2: Use point-slope form, the slope of the line and
one of the points on the line, to write the equation of
the line.
Step 3: Distribute.
Step 4: Multiply both sides of the equation by 5 to
eliminate the fractions.
Step 5: Subtract 3x from both sides of the equation.
Step 6: Add 10 to both sides of the equation.
Step 7: Multiply both sides of the equation by 21 to
create a positive leading coefficient.
Standard Form
Practice
3
1. Write the equation, y 5 x 2 4 in standard form.
4
2. Write the equation, y 1 4 5 21(x 2 3) in standard form.
3. Use point-slope form to write the equation, in standard form, of the line passing through (23, 1) and (22, 3).
1
4. Write the equation, in standard form, of the line passing through (0, 28) with a slope of − .
2
© 2014 College Board. All rights reserved.
2
SpringBoard Mini-Lesson, Algebra 1 Unit 2