Hello Anna!

I'm Ryaan and I'd be more than happy to assist you in finding the equation of the form y=mx+b.

First of all (I'm sure you already did this :) ), given the points (1,4 --> where 1 is X1 and 4 is Y1) and (2,2 --> where 2 is X2 and 2 is Y2), we need to find the slope using the slope formula (Y2-Y1) / (X2/X1). You plug in the values and you end up with (2-4) / (2-1), which is the same thing as (-2) / (1), which is -2. Therefore 'm' or the slope of this equation is m=-2.

Now, you have the equation y=-2x+b, and all you need to do is to plug either (1,4) or (2,2) for the x and y values in the equation, then isolate b and solve for b.

1. Solving with the ordered pair (1,4), that would look like: 4=-2(1) +b

                                             4=-2+b

                                             b=4-(-2)

                                             b=4+2

                                             b=6

Now that you have b=6, you can just add it into the equation, and it would look like: y=-2x+6, since the slope that we calculated is -2 and the y-intercept (b-value) is 6.

2. Solving with the ordered pair (2,2), that would look like: 2=-2(2)+b

                                                                                    2=-4+b

                                                                                    b=2+4

                                                                                    b=6

Now that you have b=6, you can just add it into the equation, and it would look like: y=-2x+6, since the slope that we calculated is -2 and the y-intercept (b-value) is 6, same as above.

Anna, I hope this helped! Please let me know if you have any further questions. Thanks! :) - Ryaan