How do you write the equation in point slope form given (2, 5) (3,10)?

2 Answers
Jun 2, 2016

#y-5=5(x-2)#

Explanation:

In general, given two points #(x_1,y_1)# and #(x_2,y_2)#
the slope can be calculated as
#color(white)("XXX")m=(y_2-y_1)/(x_2-x_1)#

and the equation of the line through these points using the point slope form is
#color(white)("XXX")(y-y_1)=m(x-x_1)color(white)("XXXXX")#see below for other forms

Given
#color(white)("XXX")(x_1,y_1)=(2,5)# and
#color(white)("XXX")(x_2,y_2)=(3,10)#

#m=(10-5)/(3-2)=5#

and the slope point form of the equation is
#color(white)("XXX")y-5=5(x-2)#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The "slope-point form" may also appear in the form:
#color(white)("XXX")y-y_2=m(x-x_2)#
or
#color(white)("XXX")(y-y_1)/(x-x_1)=m#
or
#color(white)("XXX")(y-y_2)/(x-x_2)=m#
All these forms are equivalent.

Jun 2, 2016

#y-5=5(x-2)#

graph{y=5x-5 [-10, 10, -5, 5]}

Explanation:

The point gradient/slope form is

#y-y_1=m(x-x_1)#

Were #y_1 and x_1# are points in which the line goes through, with #x_1# being the x position and #y_1# the y position which the points go through . Obviously the line goes through two of these points but lets just use #(2,5)# as the point.

Next, we need the gradient which is #(rise)/(run)#. The rise between the two points are 5, with the run being 1. therefore, the gradient is #5#

Now with these values, we substitute it into the equation to get an answer in point gradient/slope from.