Write the equation of the line in slope-intercept form given the followslope = - (5)/(4) \: y - intercept \: (0 \: - 8)

Question

write the equation of the line in slope-intercept form given the follow
`slope = - (5)/(4) \: y - intercept \: (0 \: - 8)`

Answer 1

Let's begin by identifying key information given to us:

`\begin{gathered} slope=-(5)/(4)\: \\ y-intercept\: (0\: -8) \end{gathered}`

The point-slope equation is given by:

`\begin{gathered} y-y_1=m(x-x_1) \\ y-intercept\: (0\: -8)\Rightarrow(x_1,y_1)=(0,-8) \\ (x_1,y_1)=(0,-8) \\ m=-(5)/(4) \\ y-\mleft(-8\mright)=-(5)/(4)(x-0) \\ y+8=-(5)/(4)x-0 \\ y=-(5)/(4)x-8 \\ \\ \therefore\text{The slope-intercept form is }y=-(5)/(4)x-8 \end{gathered}`