Question

What is the equation of the line that passes through (4, -1) and (-2, 3)? user: if y is 5 when x is 2.5 and y varies directly with x, find y when x is 10. user: which of the following equations is the translation 2 units down of the graph of y = |x|?

Answer 1

First find the slope of the line that passes through (4,-1) and (-2,3) by calculating "change in y" / "change in x"

So slope = -4/6 = -2/3

Remember the format y = mx + b?

So pick any of the two coordinates (I'll use (4,-1)) and sub in what you can.
-1 = -2/3(4) + b
Solve for b and you'll get 1.66666.... aka 1 2/3

So the equation is y = -2/3x + 5/3

Now for the next question.
So 5/2.5 = y/10
cross multiply and simplify and you'll get y = 20