Question

What is the equation of the line? −x−2y=4x + 2y = 4−x+4y=2x−4y=2

Answer 1

We can write the line equation as:

$y=mx+b$

And to find the values of the coefficients 'm', and 'b', we can use the intercepts(where the line cuts the x and y axis) on the graph. Looking at the graph, we have the following interceptions:

$\lbrace(0,2),(4,0)\rbrace$

Plugging those values in our equation, we have:

$\begin{cases}2=b \\ 0=4m+b\end{cases}\Rightarrow4m=-2\Rightarrow m=-\frac{1}{2}$

Writing the line equation in slope intercept form, we have the following:

$y=-\frac{1}{2}x+2$

Rewriting this equation:

$\begin{gathered} y=-\frac{1}{2}x+2 \\ \Rightarrow\frac{1}{2}x+y=2 \\ \Rightarrow x+2y=4 \end{gathered}$

And this is our final answer. The line equation is

$x+2y=4$