Question

What is the equation of the line that passes through the point (-4, 8) and has aslope of -1/4?

Answer 1

To solve the exercise you can use the point-slope formula, that is

`\begin{gathered} y-y_1=m(x-x_1) \\ \text{ Where m is the slope of the line and } \\ (x_1,y_1)\text{ is a point through which the line passes} \end{gathered}`

So, in this case, you have

`\begin{gathered} m=-(1)/(4) \\ (x_1,y_1)=(-4,8) \end{gathered}`
`\begin{gathered} y-8=(-1)/(4)(x-(-4)) \\ y-8=(-1)/(4)(x+4) \\ y-8=(-1)/(4)\cdot x-(1)/(4)\cdot4 \\ y-8=(-1)/(4)x-1 \\ \text{ Add 8 to both sides of the equation} \\ y-8+8=(-1)/(4)x-1+8 \\ y=(-1)/(4)x+7 \end{gathered}`

Therefore, the equation of the line that passes through the point (-4, 8) and has a slope of -1/4 is

`y=(-1)/(4)x+7`