Question

How do you write $x + 2y = 4$ into slope intercept form?

Answer 1

Here, we will use the general formula of slope intercept form to rewrite the given equation of a line in the slope intercept form. A slope is defined as the ratio of change in the $y$ axis to the change in the $x$ axis. It can be represented in the parametric form and in the point form.

Formula Used:
The Slope- Intercept form is given by the formula $y = mx + c$ where $m$ is the slope or the gradient and $c$ is the $y$-intercept.

Complete step by step solution:
We are given with an equation $x + 2y = 4$
The Slope- Intercept form is given by the formula $y = mx + c$ where $m$ is the slope or the gradient and $c$ is the $y$-intercept.
Now, we will rewrite the given equation of line into slope intercept form by using the general equation of slope intercept form.
$\Rightarrow 2y = - x + 4$
Now, dividing by $2$ on both the sides of the equation, we get
$\Rightarrow \dfrac{{2y}}{2} = \dfrac{{ - x}}{2} + \dfrac{4}{2}$
Now, by simplifying, we get
$\Rightarrow y = - \dfrac{1}{2}x + 2$
Thus, the slope of the line is $m = - \dfrac{1}{2}$ and the $y$-intercept of the line is $c = 2$.

Therefore, the slope intercept form of $x + 2y = 4$ is $y = - \dfrac{1}{2}x + 2$.

Note:
We know that the intercepts are defined as a graph which crosses either the $x$ axis or the $y$ axis. Also all the graphs of a function will have the intercepts, but the graph of the linear function will have both the intercepts. A point crossing the $x$-axis, it is called $x$-intercept and a point crossing the $y$-axis is called the $y$-intercept. We know that the equation of line is of the form slope-intercept form, intercept form and normal form. We will use the slope-intercept form to find the slope, $x$- intercept and $y$- intercept. The equation of line is always a linear equation with the highest degree as 1.