Question

Write an equation of a line that passes through point (4, -5) and is parallel to line x=2x+8.

-- I'd appreciate if you could explain how you got the answer also. *20 points for this one!*

Answer 1

y = mx + b
You can find the slope of the new line when you remember that parallel lines have the same slope. The slope of the given line is easily seen when you compare the given equation with the general slope-intercept form.
y = 2x - 4 compare with:
y = mx + b and you can see that the slope of the given line, and of any line parallel to it, is m = 2

So you can start your new equation off with:
y = 2x + b Now, since this line passes through the point (8, -2), then the coordintates of the point (x = 8 and y = -2) must satisfy this equation. Substitute these values of x and y into you new equation:
-2 = 2(8) + b now you can solve this for b.
-2 = 16 + b Subtract 16 from both sides of the equation.
-18 = b Now you can write your final equation:
y = 2x - 18