The linear equation in two variables in slope intercept form will be
y = mx + b
m = slope
b = y-intercept
The linear equation in two variables in standard form will be
ax + by + c = 0
a = coefficient of x
b = coefficient of y
c = constant
Convert the following equations from slope – intercept to standard form.
Problem 1 :
Slope – intercept form : y = (1/10)x – 3/5
Standard form : ______
Solution :
y = (1/10)x – 3/5
y = (1/10)x – (3/5 × 2/2)
y = (1/10)x – 6/10
Multiply 10 on both sides.
10y = x – 6
Subtract x from each sides.
-x + 10y = -6
Multiply each side by -1.
x – 10y = 6
Problem 2 :
Slope – intercept form : y = -5/7x – 1
Standard form : ______
Solution :
y = (-5/7)x – 1
y = (-5/7)x – (1 × 7/7)
y = (-5/7)x – 7/7
Multiply 7 on both sides.
7y = -5x – 7
Subtract 5x from each sides.
5x + 7y = -7
Problem 3 :
Slope – intercept form : y = -7x – 6
Standard form : ______
Solution :
y = -7x – 6
Adding 7x on both sides.
7x + y = 6
Problem 4 :
Slope – intercept form : y = (3/7)x + 3/7
Standard form : ______
Solution :
y = (3/7)x + 3/7
Multiply 7 on both sides.
7y = x + 3
Subtract x from each sides.
-x + 7y = 3
Multiply each side by -1.
x - 7y = -3
Problem 5 :
Slope – intercept form : y = (-8/9)x + 1/3
Standard form : ______
Solution :
y = (-8/9)x + 1/3
y = (-8/9)x + (1/3 × 3/3)
= (-8/9)x + 3/9
Multiply 9 on both sides.
9y = -8x + 3
Adding 8x on both sides.
8x + 9y = 3
Problem 6 :
Slope – intercept form : y = (-6/5)x – 7/5
Standard form : ______
Solution :
y = (-6/5)x – 7/5
Multiply 5 on both sides.
5y = -6x – 7
Adding 6x on both sides.
6x + 5y = -7
Problem 7 :
Slope – intercept form : y = (2/11)x – 3/11
Standard form : ______
Solution :
y = (2/11)x – 3/11
Multiply 11 on both sides.
11y = 2x – 3
Subtract 2x from each sides.
-2x + 11y = – 3
Multiply each side by -1.
2x - 11y = 3
Problem 8 :
Slope – intercept form : y = -x + 7/11
Standard form : ______
Solution :
y = -x + 7/11
y = -11x/11 + 7/11
Multiply 11 on both sides.
11y = -11x + 7
Adding 11x on both sides.
11x + 11y = 7
Problem 9 :
Slope – intercept form : y = (4/3)x – 5/3
Standard form : ______
Solution :
y = (4/3)x – 5/3
Multiply 3 on both sides.
3y = 4x – 5
Subtract 4x from each sides.
-4x + 3y = – 5
Multiply each side by -1.
4x – 3y = 5
Problem 10 :
Slope – intercept form : y = (-7/5)x – 8/5
Standard form : ______
Solution :
y = (-7/5)x – 8/5
Multiply 5 on both sides.
5y = -7x – 8
Adding 7x on both sides.
7x + 5y = – 8
May 21, 24 08:51 PM
May 21, 24 08:51 AM
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