CONVERTING BETWEEN SLOPE INTERCEPT AND STANDARD 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 :

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

2x + y = -9

2x + y + 9 = 0

So, the standard form is 2x + y + 9 = 0.

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