1.) The slope equals -5/4 because if we change the 4x+5y=-2 to a slope-intercept form then we can easily see the m (slope) and from that you switch the sign of the number and switch the numbers (ex. -1/2 = 2, 3 = -1/3). To get to the slope-intercept, you subtract 4x from both sides to get 5y=4x-2, then divide both sides by the 5 next to y to get y=4/5x-2/5.
2.) The equation would be y=1/3x+5 because if make the equation into a slope-intercept form by adding the x to both sides to get 3y=x+6 then divide both sides by 3 for y=1/3+2, then we can see the slope is 1/3 and since parallel lines have the same slope, you know the new line's slope is 1/3. Now if we put the slope into a new equation you'll get y=1/3x+b, so you then substitute the point's x and y in the equation for 5=1/3(3)+b, and then solve for b which is 5. Putting the y-intercept (b) and the slope into an equation, you get y=1/3x+5.
