# CONVERT SLOPE INTERCEPT FORM TO STANDARD FORM

## Slope Intercept Form

The linear equation in two variables in slope intercept form will be

y = mx + b

m = slope

b = y-intercept

## 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

Convert the following equations from slope – intercept to standard form.

Problem 1 :

Slope – intercept form : y = (1/10)x – 3/5

Standard form : ______

Solution :

y = (1/10)x – 3/5

y = (1/10)x – (3/5 × 2/2)

y = (1/10)x – 6/10

Multiply 10 on both sides.

10y = x – 6

Subtract x from each sides.

-x + 10y = -6

Multiply each side by -1.

x – 10y = 6

Problem 2 :

Slope – intercept form : y = -5/7x – 1

Standard form : ______

Solution :

y = (-5/7)x – 1

y = (-5/7)x – (1 × 7/7)

y = (-5/7)x – 7/7

Multiply 7 on both sides.

7y = -5x – 7

Subtract 5x from each sides.

5x + 7y = -7

Problem 3 :

Slope – intercept form : y = -7x – 6

Standard form :  ______

Solution :

y = -7x – 6

7x + y = 6

Problem 4 :

Slope – intercept form : y = (3/7)x + 3/7

Standard form :  ______

Solution :

y = (3/7)x + 3/7

Multiply 7 on both sides.

7y = x + 3

Subtract x from each sides.

-x + 7y = 3

Multiply each side by -1.

x - 7y = -3

Problem 5 :

Slope – intercept form : y = (-8/9)x + 1/3

Standard form :   ______

Solution :

y = (-8/9)x + 1/3

y = (-8/9)x + (1/3 × 3/3)

= (-8/9)x + 3/9

Multiply 9 on both sides.

9y = -8x + 3

8x + 9y = 3

Problem 6 :

Slope – intercept form : y = (-6/5)x – 7/5

Standard form :  ______

Solution :

y = (-6/5)x – 7/5

Multiply 5 on both sides.

5y = -6x – 7

6x + 5y = -7

Problem 7 :

Slope – intercept form : y = (2/11)x – 3/11

Standard form :  ______

Solution :

y = (2/11)x – 3/11

Multiply 11 on both sides.

11y = 2x – 3

Subtract 2x from each sides.

-2x + 11y = – 3

Multiply each side by -1.

2x - 11y = 3

Problem 8 :

Slope – intercept form : y = -x + 7/11

Standard form :  ______

Solution :

y = -x + 7/11

y = -11x/11 + 7/11

Multiply 11 on both sides.

11y = -11x + 7

11x + 11y = 7

Problem 9 :

Slope – intercept form : y = (4/3)x – 5/3

Standard form :  ______

Solution :

y = (4/3)x – 5/3

Multiply 3 on both sides.

3y = 4x – 5

Subtract 4x from each sides.

-4x + 3y = – 5

Multiply each side by -1.

4x – 3y = 5

Problem 10 :

Slope – intercept form : y = (-7/5)x – 8/5

Standard form :  ______

Solution :

y = (-7/5)x – 8/5

Multiply 5 on both sides.

5y = -7x – 8

7x + 5y = – 8

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