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
The linear equation in two variables in slope intercept form will be
y = mx + b
m = slope
b = y-intercept
Convert from the given standard form of a linear equation to the slope-intercept form of a linear equation.
Problem 1 :
x + 5y = 5
Solution :
Given equation is in standard form :
x + 5y = 5
To convert this into slope intercept form, we have to isolate the variable y.
Subtract x on both sides
5y = -x + 5
Divide by 5 on sides.
y = (-x/5) + (5/5)
y = (-1/5)x + 1
It exactly matches with y = mx + b.
So, the slope = -1/5 and y-intercept = 1.
Problem 2 :
3x + 2y = 4
Solution :
Given equation is in standard form :
3x + 2y = 4
To convert this into slope intercept form, we have to isolate the variable y.
Subtract 3x on both sides
2y = -3x + 4
Divide by 2 on sides.
y = (-3x/2) + (4/2)
y = (-3/2)x + 2
It exactly matches with y = mx + b.
So, the slope = -3/2 and y-intercept = 2.
Problem 3 :
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 4 :
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.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM