Question

write the standard form of the line that passes through the given point. include your work in your final answer. (6,1)and (5,4)

Answer 1

We are given two points on a line. First we need to find the slope of the line using these two points.

The given points are (6, 1) and (5, 4). The slope (m) of the line will be:

$m= \frac{4-1}{5-6} =-3$

Using the slope and the point (6,1) we can write the equation in point slope form as:

y - 1 = -3(x -6)

y = -3x + 18 + 1

y = -3x + 19

In standard form, the equation will be:

3x + y = 19

Answer 2

First, find the slope of the line thru the given pts.  It is

         4-1       3
m = ------- = ----- = -3.
         5 -6      -1

Then use the slope-intercept formula:  4 = (-3)(5) + b, so that 4 = -15 + b.  Thus, b = 19.

The equation in slope-int form is y = -3x + 19.  To change this into standard form, subtract y from both sides:    0 = -3x - y + 19.  This is "std form."