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 from the given slope intercept form of a linear equation to the standard form of a linear equation.
Problem 1 :
y = (-11x/10) - 1
Solution :
Given equation is in slope intercept form :
y = (-11x/10) - 1
y = (-11x/10) - (1/1)
LCM(10, 1) is 10.
y = (-11x/10) - (10/10)
y = (-11x - 10)/10
Multiply by 10 on both sides.
10y = -11x - 10
Add 11x and 10 on both sides.
11x + 10y + 10 = 0
So, the standard form is 11x + 10y + 10 = 0.
Problem 2 :
y = -2x - 9
Solution :
Slope intercept form :
y = -2x - 9
Add 2x on both sides.
2x + y = -9
Add 9 on both sides.
2x + y + 9 = 0
So, the standard form is 2x + y + 9 = 0.
Problem 3 :
y = (7/5)x - (1/5)
Solution :
The given equation is in slope intercept form :
y = (7/5)x - (1/5)
Both fractions are having the same denominators.
y = (7x - 5)/5
Multiply by 5 on both sides.
5y = 7x - 5
Subtract 5y on both sides
0 = 7x - 5y - 5
7x - 5y - 5 = 0
So, the required standard form is 7x - 5y - 5 = 0.
Problem 4 :
y = -x + (11/8)
Solution :
The given equation is in slope intercept form :
y = -x + (11/8)
y = -(x/1) + (11/8)
LCM (8, 1) is 8.
Multiplying the numerator and denominator of the first fraction by 8, we get
y = -(8x/8) + (11/8)
y = (-8x + 11)/8
Multiplying by 8 on both sides, we get
8y = -8x + 11
Add 8x and subtract 11 on both sides.
8x + 8y - 11 = 0
So, the required standard form of given equation is 8x + 8y - 11 = 0.
Problem 5 :
y = -x/3 + (2/9)
Solution :
The given equation is in slope intercept form :
y = -x/3 + (2/9)
LCM (3, 9) is 9.
Multiplying the numerator and denominator of the first fraction by 3, we get
y = (-x/3)(3/3) + (2/9)
y = (-3x/9) + (2/9)
y = (-3x + 2)/9
Multiplying by 9 on both sides.
9y = -3x + 2
Add 3x and subtract 2 on both sides.
3x + y - 2 = 0
So, the required standard form is 3x + y - 2 = 0.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM