7.) find the equation of the curve that passes through the point (4, 5) if its slope is given by the following equation.

Rearranging and integrating, you have

... y = ∫(4x-7)dx = 2x² -7x +c

Applying the boundary condition, you have

... 5 = 2·4² -7·4 +c

... 5 - 4 = c = 1

Then the equation of the curve is

... y = 2x² -7x +1

step-by-step explanation:

we are given

since, we have to isolate x on anyone side

so, we can move all x terms on one side

subtract both sides by 2x

add both sides by 9

divide both sides by 4

we get