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$y - 4 = 3(x - 2)$ Write the equation in slope intercept form. How do I do this?

Last updated date: 28th Feb 2024
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IVSAT 2024
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Hint:The slope intercept form of a line is given as $y = mx + c$ where “m” is the slope of the line and “c” is the intercept (mainly y intercept when $x = 0$).
Convert the given equation of line into slope intercept form with help of distributive property of multiplication and algebraic operations like addition, subtraction, multiplication etc.

Complete step by step solution:
The given equation is an equation of straight line which is expressed in
slope point form, and we are asked to convert it into slope intercept form which is given as following
$y = mx + c$ where “m” is the slope of the line and “c” is its intercept
Now, coming to the given equation of line
$y - 4 = 3(x - 2)$
Firstly opening the parentheses in the equation with the help of distributive property of multiplication, we will get
\Rightarrow y - 4 = 3x - 3 \times 2 \\
\Rightarrow y - 4 = 3x - 6 \\
Now as we can see in the general equation of line in slope intercept form, the left hand side of the equation only consists of the dependent variable and right hand side consists of independent variable as well as constant.
Adding $4$ both sides of the equation, in order to remove constant from L.H.S., we will get
\Rightarrow y - 4 + 4 = 3x - 6 + 4 \\
\Rightarrow y - 0 = 3x - 2 \\
\Rightarrow y = 3x - 2 \\
$\therefore y = 3x - 2$ is the slope intercept form of the equation $y - 4 = 3(x - 2)$

Note: Equation consists of two variables and is of one degree represents a line, and equation of a line can be written in many forms, in which slope intercept form is one of them. If we have any one form of equation of line written then we can write its other forms too by doing some simple algebra.