1. The problem statement, all variables and given/known data Suppose line tangent to graph of y=f(x) at x =3 passes through (-3, 7) & (2,-1). Find f'(3), what is the equation of the tangent line to f at 3? 2. Relevant equations I found the slope of which equals -8/5 Im not sure how to find the equation... do I do y-3=-8/5(x-3)? or is that wrong?
The tangent line passes through those two points. Since it is a LINE, you may use the equation to solve for the slope: m= (y2-y1) / (x2-x1) Once you have found the slope, use any of of the two coordinates to solve for 'c', the constant/y-intercept. Once you have the constant, simply write it in the form y=(#)x + (#). That is the equation of the tangent line at that point x=3.
Why do you keep asking? It is simple arithmetic to check whether or not (-3, 7) and (2, -1) satisfy the equations you give. Also, use parentheses to make your meaning clear. Many people would interpret "-8/5x" as "-8/(5x)". And I am not clear whether "8.2" means multiplication or "8 and 2 tenths". If you mean y= (-8/5)x+ (8)(2)= (-8/5)x+ 16 then if x= -3, y= (-8/5)(-3)+ 8.2= 24/5+ 8.2= 4. which is not 7. And if you mean y= (-8/5)x+ 8.2= (-8/5)x+ 82/10= (-8/5)x+ 41/5, then which x= -3, y= (-8/5)(-3)+ 41/5= 24/5+ 41/5= 65/5= 13, again, not 7.