How do you write the equation in slope-intercept form $y-3=2(x-6)$ ?

Hint: To solve such questions first understand the meaning of the slope-intercept form. The slope-intercept form can be written in the form of $y=mx+b$ . Here $m$ represents the slope of the graph and $b$ is a constant term. The constant represents the $y$ intercept, which is the point on the graph where the line intersects the $y$ axis.

Complete step by step answer:
The given equation is $y-3=2(x-6)$ .
First simplify the given equation by opening the parenthesis, to get,
$\Rightarrow y-3=2x-12$
Write the variables on the left-hand side of the equation and the constants on the right-hand side of the equation.
$\Rightarrow y-2x=-12+3$
Now simplify the above equation to get,
$\Rightarrow y-2x=-9$
Rearrange the above equation so that it represents the slope-intercept form, which is, $y=mx+b$ ,
$\Rightarrow y=2x-9$
The above equation now represents the slope-intercept form, with $2$ as the slope of the line and $-9$ as the point where the line intercepts the $y$ -axis.

Additional Information:
The slope of a line can be defined as the gradient or the angle that a line makes concerning a horizontal surface. There are three ways in which the slope of a line can be represented. Slope intercept form is one of the ways along with the point-slope form and standard form.

Note: Never forget to check the signs after opening the parenthesis. Remember that the slope of the line $m$ can be positive, negative, zero, or undefined, so even if the slope is coming as negative or zero, it will be correct. One must remember what does the symbol in the equation signify i.e. $m$ is the slope of the equation and is written as a coefficient of $x$ and $b$ is the $y$ intercept and is written as a constant term.