Question

what is an equation of the line that is perpendicular to y-3=4(x+2) and passes through the point (-5, 7)

Answer 1

Answer:
`y-7=-(1)/(4)(x+5)`

Explanation:

The equation of the line in Point-Slope form is:

`y-y_1=m(x-x_1)`

Where "m" is the slope and (
`x_1,y_1`) is a point on the line.

You can identify that in the equation of the line
`y-3=4(x+2)`, the slope is:

`m=4`

By definition, the slopes of perpendicular lines are negative reciprocals. Then, the slope of the other line is:

`m=-(1)/(4)`

Finally, knowing that this line passes through the point (-5, 7),you can substitute this point and the slope into the equation
`y-y_1=m(x-x_1)` to get the equation of this line:

`y-7=-(1)/(4)(x-(-5))`

`y-7=-(1)/(4)(x+5)`