CONVERTING FROM STANDARD FORM TO SLOPE INTERCEPT FORM

Standard Form

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

Slope Intercept Form

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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