Concept
Use slope and a point form to find the equation of the line.
Method
Given data
slope = -1/2
Given point = (2,-2)
Next, write the equation of a slope-point form to find the equation of a line.
[tex]\begin{gathered} \text{Slope}-po\text{int equation of a line} \\ m\text{ = }\frac{y-y_1}{x-x_1} \end{gathered}[/tex]Next, label the given data
m = -1/2
x1 = 2 and y1 = -2
Substituting m, x1 and y1 into the equation we get
[tex]\begin{gathered} m=\frac{y-y_1}{x-x_1} \\ \frac{-1}{2}\text{ = }\frac{y\text{ -(-2)}}{x\text{ - 2}} \\ \frac{-1}{2}\text{ = }\frac{y\text{ + 2}}{x\text{ -2}} \end{gathered}[/tex]Cross multiply
[tex]\begin{gathered} 2(\text{ y + 2 ) = -1 ( x - 2 )} \\ 2y\text{ + 4 = -x + 2} \\ \text{collect like terms} \\ 2y\text{ = -x + 2 - 4} \\ 2y\text{ = -x - }2 \\ \text{Divide through by 2} \\ \frac{2y}{2}\text{ = }\frac{-1}{2}x\text{ - }\frac{2}{2} \\ y\text{ = }\frac{-1}{2}x\text{ - }1 \end{gathered}[/tex]Final answer
[tex]\text{Equation of a line is: y = }\frac{-1}{2}x\text{ - 1}[/tex]
