Write the equation of the line that passes through (3, −2) and is perpendicular to y equals 3 fourths times x plus 6 period

To find the equation of a line that is perpendicular to y = 3/4x + 6 and passes through the point (3, -2), we first need to find the slope of the given line and then find the negative reciprocal to get the slope of the perpendicular line.

The slope of the line y = 3/4x + 6 is 3/4. The negative reciprocal of 3/4 is -4/3.

So, the slope of the perpendicular line is -4/3. Now we can use the point-slope form of a linear equation to find the equation of the perpendicular line:

y - y1 = m(x - x1)

where (x1, y1) is the point (3, -2) and m is the slope -4/3.

Plugging in the values, we get:

y - (-2) = -4/3(x - 3)
y + 2 = -4/3x + 4
y = -4/3x + 2

Therefore, the equation of the line that passes through (3, -2) and is perpendicular to y = 3/4x + 6 is y = -4/3x + 2.