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

2 Answers
Jun 2, 2016

y5=5(x2)

Explanation:

In general, given two points (x1,y1) and (x2,y2)
the slope can be calculated as
XXXm=y2y1x2x1

and the equation of the line through these points using the point slope form is
XXX(yy1)=m(xx1)XXXXXsee below for other forms

Given
XXX(x1,y1)=(2,5) and
XXX(x2,y2)=(3,10)

m=10532=5

and the slope point form of the equation is
XXXy5=5(x2)

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

The "slope-point form" may also appear in the form:
XXXyy2=m(xx2)
or
XXXyy1xx1=m
or
XXXyy2xx2=m
All these forms are equivalent.

Jun 2, 2016

y5=5(x2)

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

Explanation:

The point gradient/slope form is

yy1=m(xx1)

Were y1andx1 are points in which the line goes through, with x1 being the x position and y1 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 riserun. 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.