How to convert slope into standard form?

Exponents and power are the integer numbers placed on the head of the base. The integer number denotes how many times the number can be multiplied by itself. The representation of such numbers is given in the form of ‘a^x‘ where a is the base and x is the power. Those powers are generally used to express large quantities.

Note

If the given base does not carry any exponent. Then, its power will be one.

Basic laws of Exponents and powers

1. Exponents with the same base

When two exponential values with the same base are put into multiplication, then the powers are added.

a^x . a^y =a^{(x + y)}

When two exponential values with the same base are put into division, then the powers are subtracted.

a^x/a^y = a^{(x – y)}

2. Power of power

When a base with a power of power is given the powers are multiplied.

(a^x)^y = a^{x × y}

3. Different bases with the same exponents

When two different bases having the same exponents are in multiplication then, the bases are multiplied and power is taken in common.

a^x × b^x = (ab)^x

When two different bases having the same exponents are in the division then, the bases are divided and power is taken in common.

a^x/b^x=(a/b)^x

Slope

The slope is the rate of change of y with respect to x. It simply means the slope is the rate of change of one given variable with respect to the other. The slope of a line in a linear equation can be determined by putting the equation in slope-intercept form.

y = mx + b

Where, m = slope

b = y-intercept

How to convert slope into standard form?

Solution:

The standard form of a linear equation is given by

Ax + By = C

Where, A, B, and C are constants.

As mentioned above, find the slope of a line by putting the linear equation in slope-intercept form and then, So,

Subtracting Ax from both sides of the equation

Ax – Ax + By = C – Ax

By = -Ax + C

Dividing both sides by B

By/B = -Ax/B + C/B

y = -Ax + C/B

y = (-A/B)x + (C/B)

Now, the slope of a linear equation, in general, can be determined by the given formula.

m = -A/B

Sample problems

Question 1: Put the following linear equation 6x + 2y = 24 in slope-intercept form.

Solution:

Linear form = 6x + 2y = 24

Now, slope-intercept form

6x + 2y = 24

2y = -6x + 24

y = (-6/2)x + (24/2)

y = -3x + 12

Question 2: Put the following linear equation -3x + y = 4 in slope-intercept form.

Solution:

Linear form = -3x + y = 4

Now, slope-intercept form

-3x + y = 4

y = 3x + 4

Question 3: Put the following standard equation 2x + 3y = 15 in slope-intercept form.

Solution:

Linear form = 2x + 3y = 15

Now, slope-intercept form

2x + 3y = 15

3y = -2x + 15

y = (-2/3)x + 5

Question 4: Put the following standard equation 2y – 8x = -24 in slope-intercept form.

Solution:

Linear form = 2y – 8x = -24

Now, slope-intercept form

2y = 8x – 24

y = (8/2)x – 24/2

y = 4x – 12

Question 5: Put the following standard equation 4x – 12y = -9 in slope-intercept form.

Solution:

Linear form = 4x – 12y = -9

Now, slope-intercept form

4x – 12y = -9

-12y = -(4x + 9)

12y = 4x + 9

y = (4/12)x + 9/12

y = 1/3x + 3/4

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