In this section, you will learn how to convert a linear equation in slope-intercept form to standard form.
Slope intercept form |
Standard form |
y = mx + b |
ax + by = c |
Example 1 :
Write the following slope-intercept form equation of a line in standard form :
y = 3x + 1
Solution :
y = 3x + 1
Subtract 3x from each side.
-3x + y = 1
Multiply each side by -1.
3x - y = -1
Example 2 :
Write the following slope-intercept form equation of a line in standard form :
y = x/2 - 3
Solution :
y = x/2 - 3
Multiply each side by 2.
2y = x - 6
Subtract x from each side.
-x + 2y = -6
Multiply each side by -1.
x - 2y = 6
Example 3 :
Write the following slope-intercept form equation of a line in standard form :
y = (7x/2) + (1/4)
Solution :
y = (7x/2) + (1/4)
On the right side of the equation, we have the denominators 2 and 4.
Least common multiple of (2 and 4) is 4.
Multiply both sides of the equation by 4 to get rid of the denominators 2 and 4.
4y = 14x + 1
Subtract 14x from each side.
-14x + 4y = 1
Multiply each side by -1.
14x - 4y = -1
Example 4 :
Write the following slope-intercept form equation of a line in standard form :
y = (-5x/6) + (1/4)
Solution :
y = (-5x/4) + (1/6)
On the right side of the equation, we have the denominators 4 and 6.
Least common multiple of (4 and 6) is 12.
Multiply both sides of the equation by 12 to get rid of the denominators 4 and 6.
12y = -15x + 2
Add 15x to each side.
15x + 12y = 2
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