Question

Determine the slope and the y-intercept of the given equation

Answer 1

The slope of an linear equation is express as :

`\begin{gathered} y=m(x-a)+b \\ \text{ where m is the slope} \end{gathered}`

The given expression is : 8x - 5y = -20

Simplify the given expression in the general form of equation

`\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} \\ (5y)/(5)=(8x)/(5)+(20)/(5) \\ y\text{ = }(8)/(5)x+4 \end{gathered}`

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

`\begin{gathered} 8x-5y=-20 \\ 8(0)-5y=-20 \\ -5y=-20 \\ \text{ Divide both side by (-5)} \\ (-5y)/(-5)=(-20)/(-5) \\ y=4 \end{gathered}`

The y-intercept is : y = 4

Answer:

Slope : m = 8/5

y-intercept: y = 4