Answer:
[tex]y\text{ = -}\frac{5}{2}x\text{ + 3}[/tex]
Explanation:
The general equation of a straight line is:
[tex]y\text{ = mx + b}[/tex]
where m is the slope and b is the y-intercept
For the line given, the slope value is 2/5
When two lines are perpendicular, the product of their slopes is -1
Thus, from the slope of the first line, we can get the slope of the second line
Let us call the slope of the second line m2
[tex]\begin{gathered} m_2\times\text{ }\frac{2}{5}\text{ = -1} \\ \\ m_2\text{ = -}\frac{5}{2} \end{gathered}[/tex]
We have the slope of the second line and a point (2,-2) through which the line passes
We can write the equation of the line using the point-slope form as follows:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y+\text{ 2 = -}\frac{5}{2}(x-2) \\ \\ y\text{ + 2 = -}\frac{5}{2}x\text{ +5} \\ \\ y\text{ = -}\frac{5}{2}x\text{ + 5-2} \\ \\ y\text{ = -}\frac{5}{2}x\text{ + 3} \end{gathered}[/tex]
