Question

What is an equation of the line that contains the point (3,-1) and is perpendicular to the line whose equation is y=-3x+2

Answer 1

Equation of the line:
`3y=x+10`

Explanation:

If an equation of a line is perpendicular, its gradient will be such that:
`m_1 * m_2 = -1`

Since the gradient /slope of the given equation can be inferred as -3, the gradient of the perpendicular line will be
`(1)/(3)`.

Coordinates of a point on the line are (3,-1)

`(y-y_1) = m(x-x_1)\\\\(y-3) = (1)/(3) (x+1)\\\\3(y-3) = (x+1)\\3y -9= x+1\\3y = x+1+9\\3y = x+10`