Question 449100
==> Find the slope. Using points ({{{x[1]}}}, {{{y[1]}}}) and ({{{x[2]}}}, {{{y[2]}}}), the equation for slope (m) is {{{m = (y[2] - y[1])/(x[2] - x[1]). Since your points are (-9, -9) and (2, 2), your slope is {{{m = (2 - (-9))/(2 - (-9))}}}
Simplify: {{{m = (2 + 9)/(2 + 9)}}}
Add: {{{m = 11/11}}}
Simplify/Divide: {{{m = 1}}}
So, the slope of your equation is 1.
==> Next, find the equation of the line by plugging in the slope and coordinates of one of the points in to point-slope form, or {{{y - y[1] = m(x - x[1])}}}. For ({{{x[1]}}}, {{{y[1]}}}), I am going to choose (-9, -9), but you could also use (2, 2). {{{y - (-9) = 1(x - (-9))}}}
Simplify: {{{y + 9 = 1(x + 9)}}}
Since 1*a = a, you can simplify 1(x + 9) into just x + 9: {{{y + 9 = x + 9}}}
Subtract 9 from both sides: {{{y = x}}}
That is in y = mx + b form, as it can also be seen as y = 1x + 0.
***THEREFORE, YOUR FINAL ANSWER IS {{{y = x}}}