The slope of an linear equation is express as :
[tex]\begin{gathered} y=m(x-a)+b \\ \text{ where m is the slope} \end{gathered}[/tex]The given expression is : 8x - 5y = -20
Simplify the given expression in the general form of equation
[tex]\begin{gathered} 8x-5y=-20 \\ \text{Add 5y on both side} \\ 8x-5y+5y=-20+5y \\ 8x=-20+5y \\ \text{Add 20 on both side} \\ 8x+20=-20+5y+20 \\ 8x+20=5y \\ or \\ 5y=8x+20 \\ \text{ Divide both side by 5} \\ \frac{5y}{5}=\frac{8x}{5}+\frac{20}{5} \\ y\text{ = }\frac{8}{5}x+4 \end{gathered}[/tex]On comparing with the general equation, we get m = 8/5
Slope , m = 8/5
For the y-intercept
Substitute the x = 0 in the expression and the solve for the y, the resultant expression is the y -intercept
[tex]\begin{gathered} 8x-5y=-20 \\ 8(0)-5y=-20 \\ -5y=-20 \\ \text{ Divide both side by (-5)} \\ \frac{-5y}{-5}=\frac{-20}{-5} \\ y=4 \end{gathered}[/tex]The y-intercept is : y = 4
Answer:
Slope : m = 8/5
y-intercept: y = 4