How do you write an equation of a line that passes through (4,9) , (-2,-6)?

↳Redirected from "Suppose that I don't have a formula for #g(x)# but I know that #g(1) = 3# and #g'(x) = sqrt(x^2+15)# for all x. How do I use a linear approximation to estimate #g(0.9)# and #g(1.1)#?"
1 Answer
Faizan B.
Apr 3, 2015

I will use the point-slope form of a line (#y-y_1=m(x-x_1)#):

Point 1 will be (4,9)
Point 2 will be (-2,-6)

Calculating the slope: #m=(∆y)/(∆x)=(y_2-y_1)/(x_2-x_1)=(9-(-6))/(4-(-2))=(9+6)/(4+2)=15/6=(3(5))/(3(2))=color(red)(5/2)#

So: #y-(9)=(5/2)(x-4)#

Now, I will transform the equation from point-slope to slope-intercept (#y=mx+b#) form. Remember, changing the form of a line's equation does not change the line. It simply rewrites the variables in a different way.

#y-(9)=(5/2)(x-4)#
#y=(5/2)(x-4)+9#
#y=5/2x-20/2+9#
#y=5/2x-10+9#
#y=5/2x-1#

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