We are given the following equation of a line:
[tex]5x+-2y=8[/tex]We are asked to determine the y-intercept. To do that we need to convert the equation into the following form:
[tex]y=mx+b[/tex]Where "b" is the y-intercept.
To convert the equation we will solve for "y" first by subtracting "5x" from both sides:
[tex]-2y=8-5x[/tex]Now, we divide both sides by -2:
[tex]y=\frac{8}{-2}-\frac{5x}{-2}[/tex]Now we simplify the fractions:
[tex]y=-4+\frac{5}{2}x[/tex]Therefore, the y-intercept is -4.
