Converting from slope intercept to standard form :
Here we are going to see how to convert the given equation from slope intercept form standard form.o Standard form of the equation is ax + by = c, where a, b and c are integers.
Slope intercept form |
Standard form |
y = mx + b |
ax + by = c |
Now let us look into some example problems to understand how to convert the given equation into standard form.
Example 1 :
Write the following equation in standard form using integers
y = 3x + 1
Solution :
Here the above given equation is in slope intercept form (y = mx + b).
To convert the given equation into standard form, we have to bring x and y terms on the left side of the equal sign and constant to the the right side.
y = 3x + 1
Subtract 3x from both sides
y - 3x = 3x - 3x + 1
-3x + y = 1
Multiply negative sign to both sides
-(-3x + y) = -1
3x - y = -1
Hence the standard form of the given equation is
3x - y = -1
Example 2 :
Write the following equation in standard form using integers
y = (1/2)x - 3
Solution :
Here the above given equation is in slope intercept form (y = mx + b).
y = (x/2) - (3/1)
Take L.C.M to the right side
y = (x/2) - (3/1) (2/2)
y = (x - 3)/2
Multiply both sides by 2.
2y = x - 3
Subtract both sides by 2y
2y -2y = x - 2y - 3
0 = x - 2y - 3
Add both sides by 3
0 + 3 = x - 2y + 3
3 = x - 2y
x - 2y = 3
Hence the standard form of the given equation is
x - 2y = 3
Example 3 :
Write the following equation in standard form using integers
y = (7x/2) + (1/4)
Solution :
y = (7x/2) + (1/4)
Take L.C.M to the right side
y = (7x/2) (2/2) - (1/4)
y = (14x/4) - (1/4)
y = (14x - 1)/4
Multiply both sides by 4.
4y = 14x - 1
Subtract both sides by 4y
4y - 4y = 14x - 4y - 1
0 = 14x - 4y - 1
Add both sides by 1
0 + 1 = 14x - 4y - 1 + 1
1 = 14x - 4y
14x - 4y = 1
Hence the standard form of the given equation is
14x - 4y = 1
Example 4 :
Write the following equation in standard form using integers
y = (-2x/5) + (1/10)
Solution :
y = (-2x/5) + (1/10)
Take L.C.M to the right side
y = (-2x/5) (2/2) + (1/10)
y = (-4x/10) + (1/10)
y = (-4x + 1)/10
Multiply both sides by 10.
10y = -4x + 1
Add both sides by 4x
10y + 4x = -4x + 4x + 1
10y + 4x = 1
4x + 10y = 1
Hence the standard form of the given equation is
4x + 10y = 1
After having gone through the stuff given above, we hope that the students would have understood, "Converting from slope intercept to standard form".
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