Question

What is an equation of the line that passes through the point left bracket, 2, comma, 6, right bracket(2,6) and is perpendicular to the line x, plus, 4, y, equals, 8x+4y=8?

Answer 1

The equation of the line perpendicular to the line 8x + 4y = 8 and passing through the point (2,6) is y = 1/2x + 5.

Step-by-step explanation:

The student is asking for the equation of a line that is perpendicular to another line and passes through a given point. The original line's equation is 8x + 4y = 8 which simplifies to y = -2x + 2, giving it a slope of -2.

A line perpendicular to this must have a slope that is the negative reciprocal, which is 1/2.

Using the point-slope form of the line equation, and the point (2, 6), we begin with y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point.

Substituting in our values we get y - 6 = 1/2(x - 2) or y = 1/2x + 5 after rearranging.