Question

what is the equation of a line perpendicular to y=-1/3x+3

Answer 1

The given equation of the line is y = -1/3x + 3.

To find the equation of a line perpendicular to this line, we first need to determine the slope of the given line.

The slope-intercept form of a line is y = mx + b, where m represents the slope. In this case, the slope is -1/3.

Perpendicular lines have slopes that are negative reciprocals of each other. This means that the slope of the line perpendicular to y = -1/3x + 3 will be the negative reciprocal of -1/3.

The negative reciprocal of -1/3 is 3/1, or simply 3.

Now that we have the slope of the perpendicular line, we can construct the equation of the line using the point-slope form:

y - y1 = m(x - x1)

where (x1, y1) represents a point on the line. Any point on the line can be used.

Let's use the y-intercept of the given line, which is (0, 3).

Substituting the values into the equation, we have:

y - 3 = 3(x - 0)

Simplifying further:

y - 3 = 3x

Adding 3 to both sides to isolate y:

y = 3x + 3

Therefore, the equation of the line perpendicular to y = -1/3x + 3 is y = 3x + 3.