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 :
2x + y = 4
Solution :
Given equation is in standard form :
2x + y = 4
To convert this into slope intercept form, we have to isolate the variable y.
Subtract 2x on both sides
y = -2x + 4
It exactly matches with y = mx + b.
So, the slope = -2 and y-intercept = 4.
Problem 4 :
4x – 2y = 6
Solution :
Given equation is in standard form :
4x – 2y = 6
To convert this into slope intercept form, we have to isolate the variable y.
Add 2y and subtract 6 on both sides.
4x - 6 = 2y
2y = 4x - 6
Divide by 2 on both sides.
y = (4x/2) - (6/2)
y = 2x - 3
It exactly matches with y = mx + b.
So, the slope = 2 and y-intercept = -3.
Problem 5 :
8x – 4y = 16
Solution :
Given equation is in standard form :
8x – 4y = 16
To convert this into slope intercept form, we have to isolate the variable y.
Add 2y and subtract 6 on both sides.
4x - 6 = 2y
2y = 4x - 6
Divide by 2 on both sides.
y = (4x/2) - (6/2)
y = 2x - 3
It exactly matches with y = mx + b.
So, the slope = 2 and y-intercept = -3.
Problem 6 :
3x + 4y = 4
Solution :
3x + 4y = 4
Subtract 3x on both sides.
4y = -3x + 4
Divide by 4 on both sides.
y = (-3/4)x + (4/4)
y = (-3/4)x + 1
Slope = -3/4 and y-intercept = 1
Problem 7 :
9x – 4y = -16
Solution :
Add 4y on both sides.
9x = -16x + 4y
Add 16 on both sides.
9x + 16 = 4y
4y = 9x + 16
Divide by 4 on both sides.
y = (9/4) x + (16/4)
y = (9/4) x + 4
Slope = 9/4 and y-intercept = 4.
Problem 8 :
2x – 5y = 10
Solution :
2x – 5y = 10
Add 5y on both sides.
2x = 5y +10
Subtract 10 on both sides.
2x - 10 = 5y
Divide by 5 on both sides.
y = (2/5)x - (10/5)
y = (2/5)x - 2
Slope = 2/5 and y-intercept = -2
Problem 9 :
3x + 5y = -25
Solution :
3x + 5y = -25
Subtract 3x on both sides.
5y = -3x - 25
Divide by 5.
y = (-3/5)x - (25/5)
y = (-3/5)x - 5
Problem 10 :
7x – y = 4
Solution :
7x – y = 4
Add y on both sides.
7x = y + 4
Subtract 4 on both sides.
7x - 4 = y
y = 7x - 4
Slope = 7 and y-intercept = -4.
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