Question

What is the equation of the line that passes through the points (2,-2) and has a slope of -1/2

Answer 1

Given the point (2,-2) and the slope m = -1/2, we can find the equation of the line using the point-slope formula:

`\begin{gathered} (x_0,y_0)=(2,-2)_{} \\ m=-(1)/(2) \\ Equation\colon \\ y-y_0=m(x-x_0) \\ \Rightarrow y-(-2)=-(1)/(2)(x-2)=-(1)/(2)x+(2)/(2)=-(1)/(2)x+1_{} \\ \Rightarrow y+2=-(1)/(2)x+1 \\ \Rightarrow y=-(1)/(2)x+1-2=-(1)/(2)x-1 \\ y=-(1)/(2)x-1 \end{gathered}`

therefore, the equation of the line is y = -1/2x -1