Question

What is the equation of the line passing through (−5,−3) and perpendicular to the line representing the equation y=−57x+2

Answer 1

Answer:
`y=(1)/(57)x-(166)/(57)`

Explanation:

In order to find a line that is perpendicular to the given equation, we must do 2 things. Perpendicular lines intersect and create a right angle. Therefore we have to find the reciprocal and change the sign of the slope.

Slope: -57

Reciprocal:
`-(1)/(57)`

Change sign:
`(1)/(57)`

Now, we know that the slope of the perpendicular line should be
`(1)/(57)`. We are also given a point of the perpendicular line, as all we have to do is plug that in and solve for the y-intercept.

`-3=(1)/(57)(-5)+b` [Multiply]

`-3=-(5)/(57) +b` [Add both sides by
`(5)/(57)`]

`b=-(166)/(57)`

With the y-intercept, we can fill in the equation for the new line.

`y=(1)/(57)x-(166)/(57)`