Question

How do you write \[x + 2y = 4\] into slope intercept form?

Answer 1

Hint: 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.