Question

A given line has the equation 2x + 12y = −1.

What is the equation, in slope-intercept form, of the line that is perpendicular to the given line and passes through the point (0, 9)?

y=( )x+9

Answer 1

By using the point-slope formula, the equation of the perpendicular line is y = 12x + 9.

Step-by-step explanation:

To find the equation of a line perpendicular to the given line and passing through the point (0, 9), we need to determine the slope of the given line first.

The given line has the equation 2x + 12y = -1.

To find the slope, we'll rearrange the equation to y = mx + b form, where m represents the slope.

Subtracting 2x from both sides and then dividing by 12, we get y = -(1/12)x - (1/12).

The slope of the given line is -(1/12). Since the slope of a line perpendicular to another line is the negative reciprocal of its slope, the slope of the perpendicular line is 12.

Using the point-slope formula, y - y1 = m(x - x1), we can substitute the slope (m = 12) and the given point (x1 = 0, y1 = 9) in the equation to find the equation of the perpendicular line.

After substituting the values, the equation becomes y = 12x + 9.

Answer 2

Step-by-step explanation:

Perpendicular lines have slopes that are opposite reciprocals of each other. In order to write the equation of a line perpendicular to the one given, we need to find the slope of the given line and then take the opposite reciprocal of it. The current form the line is in does not give us a clear idea of what the slope is. We will first put the given line into slope-intercept form (right now it's in standard form, which is not helpful for anything at all!). Solving the given equation for y:

12y = -2x - 1 and

`y=-(1)/(6)x-(1)/(12)` (notice I reduced the slope's fraction from -2/12)

That means that the slope of the given line is -1/6. So the perpendicular slope is positive 6/1 or just 6.

Using that slope and the given point in point-slope form to write the equation:

y - 9 = 6(x - 0) and

y - 9 = 6x - 0 and

y = 6x + 9

There you go!