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Isolating variables is a crucial step in solving linear equations. This means manipulating the equation so that the variable you are solving for stands alone on one side.

In our example equation, we want to solve for the variable *y*. We begin by rewriting the provided equation \(\frac{y-k}{m}=x-h\) in a more manageable form.

The next step is to isolate the variable *y* by gradually 'undoing' other operations that surround the variable. This process often involves moving terms to different sides of the equation or reversing operations like addition, subtraction, multiplication, and division.

By isolating *y*, we simplify our problem and make the equation more straightforward to solve.

Fractions can make equations look complex, but there's a straightforward way to remove them. This is done by multiplying every term by the denominator of the fraction.

Let's see how we remove the fraction in \(\frac{y-k}{m}=x-h\)

• Multiply both sides of the equation by *m* to eliminate the fraction, resulting in \(\frac{y-k}{m} \times m = (x-h) \times m\).

This multiplication simplifies to \(y-k = m(x-h)\).

Now, the fraction is removed, making it easier to isolate the variable *y*. This step is essential as it transforms a potentially complex fraction problem into a simpler form.

Remember, always multiply each term by the denominator to maintain the equation's balance and get rid of fractions.

Algebraic manipulation involves applying basic algebraic operations to both sides of the equation to simplify and solve it.

After removing the fraction in \(y-k=m(x-h)\), the next step is to isolate the variable *y*. To do this:

• Add *k* to both sides of the equation: \ y-k+k=m(x-h)+k \
• This simplifies to \ y = m(x-h) + k \, isolating *y* on one side.

Each algebraic manipulation step helps peel away the layers around the variable, slowly working towards the solution.

By methodically applying operations like addition, subtraction, multiplication, or division, you can simplify even the most complex-looking equations.

Always ensure you perform each operation equally on both sides of the equation to maintain its balance.