We want to find the equation of the line with given slope and y-intercept.
The slope-intercept form of a line is:
[tex]y=mx+b[/tex]Where
m is the slope
b is the y-intercept (y-axis cutting point)
We are given the slope and y-intercept, so we simply substitute it. Steps are shown below:
[tex]\begin{gathered} y=mx+b \\ y=\frac{2}{5}x+(-7) \\ y=\frac{2}{5}x-7 \end{gathered}[/tex]The equation of the line is:
[tex]y=\frac{2}{5}x-7[/tex]