Question

How do you write the equation \[y + 3 = \dfrac{1}{2}\left( {x + 4} \right)\] in slope intercept format?

Answer 1

Hint: The slope intercept form is probably the most frequently used way to express equation of a line. To be able to use slope intercept form, all that you need to be able to do is
1) Find the slope of a line
2) Find the y-intercept of a line.

Complete step-by-step solution:
The given equation is
\[ \Rightarrow y + 3 = \dfrac{1}{2}\left( {x + 4} \right)\]
Change this equation to the form
$ \Rightarrow y = mx + b$
For that, multiply terms inside the brackets
We get,
$ \Rightarrow y + 3 = \dfrac{x}{2} + \dfrac{4}{2}$
On cancelling the multiple of$2$, we get
$ \Rightarrow y + 3 = \dfrac{x}{2} + 2$
Now on bringing the number $3$ to the RHS, we get
$ \Rightarrow y = \dfrac{x}{2} + 2 - 3$
On subtracting the terms, we get
$ \Rightarrow y = \dfrac{x}{2} - 1$
We can also rewrite it as
$ \Rightarrow y = \dfrac{1}{2}x - 1$

Slope intercept form of the given line is $y = \dfrac{1}{2}x - 1$

Note: The ordered pairs given by a linear function represent points on a line.
Linear functions can be represented in words, function notation, tabular form and graphical form.
The rate of change of a linear function is also known as the slope.
An equation in slope-intercept form of a line includes the slope and the initial value of the function.
The initial value, or $y$ -intercept, is the output value when the input of a linear function is zero. It is the $y$ value of the point where the line crosses the $y$ axis.
An increasing linear function results in a graph that slants upward from left to right and has a positive slope.
A decreasing linear function results in a graph that slants downward from left to right and has a negative slope.
A constant linear function results in a graph that is a horizontal line.
Analyzing the slope within the context of a problem indicates whether a linear function is increasing, decreasing, or constant.
The slope of a linear function can be calculated by dividing the difference between y-values by the difference in corresponding x-values of any two points on the line.
The slope and initial value can be determined given a graph or any two points on the line.
One form of a linear function is slope-intercept form.