Question

Pls help me with this thank u

Answer 1

`y=-5x+22`

Explanation:

If two lines are perpendicular to each other, the product of their slopes will be -1.

Therefore, the slope (m) of the line that is perpendicular to
`y=(1)/(5)x-3` is:

`\begin{aligned}\implies m \cdot (1)/(5) & =-1\\m & =-5\end{aligned}`

Using the point-slope form of a linear equation, with the given point (4, 2) and the calculated slope of -5:

`\begin{aligned}y-y_1 & =m(x-x_1)\\\implies y-2 & = -5(x-4)\\y-2 & = -5x+20\\y & = -5x+22\end{aligned}`

Therefore, the equation of a line that passes through the point (4, 2) and is perpendicular to the line
`y=(1)/(5)x-3` is:

`\Large \boxed{y=-5x+22}`