We can write the line equation as:
[tex]y=mx+b[/tex]
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:
[tex]\lbrace(0,2),(4,0)\rbrace[/tex]
Plugging those values in our equation, we have:
[tex]\begin{cases}2=b \\ 0=4m+b\end{cases}\Rightarrow4m=-2\Rightarrow m=-\frac{1}{2}[/tex]
Writing the line equation in slope intercept form, we have the following:
[tex]y=-\frac{1}{2}x+2[/tex]
Rewriting this equation:
[tex]\begin{gathered} y=-\frac{1}{2}x+2 \\ \Rightarrow\frac{1}{2}x+y=2 \\ \Rightarrow x+2y=4 \end{gathered}[/tex]
And this is our final answer. The line equation is
[tex]x+2y=4[/tex]
