tangent

The given parabola is 2 x ² = 7 y

differentiating with respect to x ..

7 dy/dx = 4x

or dy/dx = 4x/7

but dy/dx = 0.5 so 4x/7 = 0.5

or x = 7/8 putting this value of x in parabola we get y = 7/32

so the required tangent at (7/8, 7/32) with slope 0.5 is

y - 7/32 = 0.5 (x - 7/8)

or 16 x - 32 y - 7 = 0