Question

find the equation of tangent where m=-1 and passing through the point (pi/4, 3/2)

Answer 1

To find the equation of a tangent line, we need both the slope (m) and a point that the tangent line passes through.

Given that the slope (m) is -1 and the point it passes through is (π/4, 3/2), we can use the point-slope form of a linear equation:

y - y1 = m(x - x1)

Substituting the known values, we have:

y - 3/2 = -1(x - π/4)

Expanding the equation gives:

y - 3/2 = -x + π/4

Rearranging the equation to put it in slope-intercept form (y = mx + b), we get:

y = -x + π/4 + 3/2

Combining like terms, we have:

y = -x + π/4 + 6/4

Simplifying further:

y = -x + (π + 6)/4

Thus, the equation of the tangent line with a slope of -1 passing through the point (∏/4, 3/2) is y = -x + (π + 6)/4.