Question

write an equation of the line perpendicular to the given line that contains P in point slope form? P (4,8) y=4x-7

Answer 1

• y - 8 = -1/4(x - 4)

Explanation:

Perpendicular lines have negative-reciprocal slopes.

The line contains point P(4, 8)

Point slope form:

• y - y₁ = m(x - x₁)

Given line:

• y = 4x - 7

The slope of the perpendicular line is m = -1/4.

The line in point-slope form is:

• y - 8 = -1/4(x - 4)

Answer 2

y - 8 = -1/4(x - 4)

Explanation:

If two lines are perpendicular to each other, they have opposite slopes.

The first line is y = 4x - 7. Its slope is 4. A line perpendicular to this one will have a slope of -1/4, the reciprocal (opposite) of the given equation.

Plug this value (-1/4) into your standard point-slope equation of y - y₁ = m(x - x₁)

y - y₁ = -1/4(x - x₁)

To find x₁ and y₁, we want to plug in a value that we know is on this line: in this case, it is P (4, 8). Plug in the x and y values into the x₁ and y₁ of the standard equation.

y - 8 = -1/4(x - 4)

This equation is perpendicular to your given equation (y = 4x - 7) and contains point P (4, 8)

Hope this helps!