Question

Find the slope and the y-intercept for the following linear function-6x + 5y = -10

Answer 1

Given the linear function below,

`-6x+5y=-10`

The general form of the equation of a straight line in the "slope-intercept form" is given below as,

`\begin{gathered} y=mx+c \\ \text{Where m is the slope} \\ c\text{ is the y-intercept} \end{gathered}`

To find the slope and y-intercept of the equation given

Making y the subject below, to find the slope-intercept form

`\begin{gathered} -6x+5y=-10 \\ 5y=6x-10 \\ \text{Divide both sides by 5} \\ (5y)/(5)=(6x-10)/(5) \\ y=(6)/(5)x-2 \end{gathered}`

Since m is the slope and c is the y intercept, to find the slope and intercept of the above equation,

`\begin{gathered} y=mx+c \\ y=(6)/(5)x-2 \\ m=(6)/(5),c=-2 \end{gathered}`

Hence, the slope, m = 6/5 and the y-intercept, c = -2