Take 2 points on the graph of y=x+2 (you don't need to graph just plug in any number for x and solve for y to get each point) then to find slope you use (Y2-Y1)/(X2-X1) Where Y2 equals the point with the larger X. Y1 is the Y value from the point with the smaller X value out of the two points you selected. X2 is the larger X value and X1 is the smaller X value.
For your problem I would select two values for X just any points will work, but I choose 1 and 4. I plug those into your equation, y=1+2 y=3, and y=4+2 y=6 so I have the two points now. (1,3) and (4,6). Now I can find slope. (6-3)/(4-1)=3/3=1
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x+2y = 2 2y = -x+2 y = -0.5x+1 Therefore the slope is -0.5 and the y intercept is 1
y = x + 2 Slope-intercept form is y = mx + b The slope, m, would be 1 and the y-intercept, b, would be 2
If: y = -2/3x+2 then the slope is -2/3 and the y intercept is 2
x + 5y = 10 5y = -x + 10 y = -x/5 + 2 m = -1/5 or .2
The whole line 'shifts up' by two units, and is parallel to the original line (same slope)