Write an equation of the line containing the given point and parallel to the given line. Express your answer in the form y=mx+b.

(-5,8); 8x = 3y + 2

The equation 8x = 3y + 2 is the equation of a linear function. Lets rewrite it in the form y = mx +  b where b is the y-intercept :

3y + 2 = 8x

3y = 8x - 2

y = (8/3)x - (2/3)

And so here, the slope (or gradient) is 8/3 and the y intercept is -2/3

A parallel line to this linear function should have the same y-intercept but a different slope. And since this line passes through x = -5 and y = 8, we can find the new slope by replacing the value :

y = mx - 2/3

8 = m*(-5) - 2/3

8+2/3 = -5m

26/3 = - 5m

-130/3 = m

An equation of the line containing the given point (-5,8) and parallel to the given line would be :

y = (-130/3)x -2/3

i hope this is what you were looking for.

see attached graph