Question

How do you identify the slope and y-intercept for $x - 2y = 4?$

Answer 1

Hint: In the above question, we have an equation. And we have to find the slope and $y - $ intercept. First of all, we will write the given equation into the standard form and then we will compare the given equation with the slope-intercept form of the equation of the line.
Slope intercept form of a line having slope $'m'$ and the $y - $ intercept equals to $'b'$ is $y = mx + b$ .

Complete step-by-step answer:
The given equation: $x - 2y = 4$ .
We should first understand their meaning to find the value of slope and $y - $ intercept.
The change of $y - $ value over the change of $x - $ value is known as the slope of the line. The slope of the line is also known as the gradient of the line. We can also call it ‘Rise over run’.
Now the intercept of a line is the point where the line touches the $x$ or $y$ axis.
Let us write the slope-intercept form:
$y = mx + b$, where $m$ is the slope of the equation and $b$ is the $y - $ intercept.
We will rearrange the given equation in the question and can write it as:
$ \Rightarrow - 2y = - x + 4$
Now we will divide the left-hand side and right-hand side of the whole equation by $ - 2$ :
$ \Rightarrow \dfrac{{ - 2y}}{{ - 2}} = \dfrac{{ - x}}{{ - 2}} + \dfrac{4}{{ - 2}}$
On simplifying, we can write this as:
$ \Rightarrow y = \dfrac{1}{2}x - 2$
By comparing this from the given equation, we have
$m = \dfrac{1}{2}$ and the value of $b = - 2$ .
Hence the slope of the given equation is $\dfrac{1}{2}$.
We can see the graph of the line $x-2y=4$ along with its slope in the below figure.

Note: We should know that if the value of constant i.e., $b = 0$ , then it means that the line will pass through the origin and will have the value of $x$ and $y$ intercepts equal.
The above slope-intercept form is of the straight line.
We should also know the standard form of a linear equation i.e.
$Ax + By = C$ , where $A,B$ are the constants.