Various equation forms, continued.

We
now will provide proof that the line shown in the graph can be represented by
an equation in three different forms. Since all the equation forms are equal to
one another they can be converted from one form to another and still represent
the line. Notice also that if we are given two sets of (x,y) points on the line
we can calculate the line slope and y intercept. This is all the information we
need to fully describe the line in any of the three equation formats.

·
**Convert two points (3,2) and (8,4) to point slope
equation form.**

(y2 - y1) / (x 2 - x1)
:: Find the slope of the line
between two points.

(4 - 2) / (8 - 3)
:: Enter the values of the two
points.

2/5
:: This is the slope or m of the
line.

(y - 2) / (x
- 3) = 2/5 :: Replace the y2 = 4 and x 2
= 8 points
with y and x.

((y -2)/(x
-3)) * (x -3) = 2/5 * (x -3) :: Multiply
both sides by (x-3)

y - 2 = 2/5x + .8 ::** Point
slope form** y - y1 = m(x - x1)

·
**Convert the point slope form of the equation to the
slope intercept form.**

y
- 2 = 2/5(x - 3)
::** Point slope form** y - y1
= m(x - x1)

y - 2 +2 = 2/5(x - 3) +2 :: Add
+2 to each side

y = 2/5*x - 2/5*3 + 2 :: Multiply
the term (x-3) by 2/5

y = 2/5*x - 1.2 + 2
:: Now add
-1.2 and +2

y = 2/5x - .8
::
Change the decimal to a fraction

y = 2/5x - 4/5
::
**Slope intercept form**** **y = mx + b

·
**Convert the slope intercept form to the standard
form.**

y
= 2/5x - 4/5
:: **Slope intercept form **y = mx + b

y * 5 = (2/5x)*5 - (4/5)*5
::
Multiply each side by 5

5y = 2x - 4
:: Move 2x to the left side and change the
sign.

5y - 2x = - 4
:: **Standard form** Ax
+ By = C

·
**Convert standard form to point slope form.**

2x
- 5y = - 4
:: ** Standard form** of Ax + By = C

2x + 4 = 5y :: Move the -4 to the left and 5y to the right.

5y = 2x + 4 :: Reverse
the order to get 5y on the left.

5y/5 = (2x + 4)/5
:: Convert
the fraction 4/5 to a decimal

y = 2/5x + .8 ::
** Point
slope form.** y - y1 = m(x - x1)

·
Given: (x_{1} , y_{1}) and (x_{2}, y_{2})
representing two points on a line;

use **(y - y _{1})/(x - x_{1}) = (y_{2
}- y_{1}) / (x_{2 }- x_{1})** to solve
for the lines equation in

·
Given: (x, y) and *m* representing one point on
the line and the slope of the line;

use **(y - y _{1})/(x - x_{1}) = m** and solve
for y giving the

·
Given: *m* and b representing the slope of the line and
the y intercept;

use **y = mx + b** to give the **slope intercept**
form of the equation.

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