Given the points : ( 4 , 0 ) and ( 0 , 4 )
The general slope - intercept form is :
[tex]y=m\cdot x+b[/tex]Where m is the slope and b is y- intercept
The slope is :
[tex]slope=m=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}=\frac{4-0}{0-4}=\frac{4}{-4}=-1[/tex]Y- intercept is the value of y when x = 0 , which is the given point ( 0 , 4 )
So,
[tex]b=4[/tex]Substitute with m and b
so, the equation of the line is :
[tex]\begin{gathered} y=-1\cdot x+4 \\ \\ y=-x+4 \end{gathered}[/tex]