What is the equation of the line between #(0,0)# and #(2,-10)#?

↳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)#?"
2 Answers
Camilleon
Apr 29, 2018

The slope is -5.

Explanation:

To find this answer, we'll be using the point slope formula:

#(Y_2 - Y_1)/(X_2 - X_1) = m# , where #m# is the slope.

#(0, 0)# #(X_1, Y_1)#
#(2, 10)# #(X_2, Y_2)#

Now, plug-in the variables:

#(-10 - 0)/(2-0)# = #m#

Subtract.

#-10/2# = #m#

Simplify.

#-5/1# = #m#

The slope is #-5#.

#(y = -5x)#

Serena D.
Apr 29, 2018

#y=-5x#

Explanation:

Slope-intercept form of an equation: #y=mx+b#, where #m# is the slope and #b# is the y-intercept

Let's first find the slope using the points #(x_1, y_1)# and #(x_2, y_2)#: #(y_2-y_1)/(x_2-x_1)#

#(-10-0)/(2-0)#

#(-10)/2#

#-5#

Our equation is currently #y=-5x+b#

The y-intercept is in the format #(0, b)#. The point #(0, 0)# is the y-intercept in this case.

#y=-5x+0#

#y=-5x#

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