The equation of a line in slope-intercept form, is:
[tex]y=mx+b[/tex]Where m is the slope of the line and b is the y-intercept.
In the given equation:
[tex]y=\frac{2}{5}x-4[/tex]The slope is equal to 2/5 and the y-intercept is equal to -4.
Since the y-intercept is equal to -4, this means that the line must pass through the point (0,-4), since it cuts the y-axis at y=-4.
On the other hand, we can calculate the coordinates of another point on the line choosing a value for x and figuring out the corresponding value of y using the given equation.
For instance, let's see which value of y corresponds to x=5:
[tex]\begin{gathered} y=\frac{2}{5}(5)-4 \\ =2-4 \\ =-2 \end{gathered}[/tex]Then, the point (5,-2) must belong to the line.
On the graphs, search for one where the line passes throught the points (0,-4) and (5,-2):
