Solution:
Given:
[tex]\begin{gathered} y-intercept=-3 \\ Point\text{ \lparen5,-1\rparen} \end{gathered}[/tex]
Since the y-intercept is -3, the line will pass through the y-intercept. The y-intercept is the value of y when x = 0. Hence, the y-intercept is (0,-3)
Thus, the line passes through points (0,-3) and (5,-1)
The equation of a line through two points is given by;
[tex]\begin{gathered} \frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1} \\ \\ where: \\ x_1=0,y_1=-3 \\ x_2=5,y_2=-1 \\ \\ Hence, \\ \frac{y-(-3)}{x-0}=\frac{-1-(-3)}{5-0} \\ \frac{y+3}{x}=\frac{-1+3}{5} \\ \frac{y+3}{x}=\frac{2}{5} \\ \\ Cross\text{ multiplying;} \\ y+3=\frac{2}{5}x \\ y=\frac{2}{5}x-3 \end{gathered}[/tex]
Therefore, the equation of a line that has a y-intercept of -3 and passes through the point (5,-1) is;
[tex]y=\frac{2}{5}x-3[/tex]
