Question 236963
<pre>What is the point slope form with the table 
(X) 3,5, 7, 9
(Y)-6,2,10,18
<pre><font size = 4 color = "indigo"><b>
Let's plot those points and see if they are in a straight line:

{{{drawing(278.6,600,-2,11,-8,20, graph(278.6,600,-2,11,-8,20), 

line(3+.1,-6,3-.1,-6),line(3,-6+.1,3,-6-.1),line(3+.1,-6+.1,3-.1,-6),line(3+.1,-6-.1,3-.1,-6+.1),
line(5+.1,2,5-.1,2),line(5,2+.1,5,2-.1),line(5+.1,2+.1,5-.1,2-.1),line(5+.1,2-.1,5-.1,2+.1),
line(7+.1,10,7-.1,10),line(7,10+.1,7,10-.1),line(7+.1,10+.1,7-.1,10-.1),line(7+.1,10-.1,7-.1,10+.1),
line(9+.1,18,9-.1,18),line(9,18+.1,9,18-.1),line(9+.1,18+.1,9-.1,18-.1),line(9+.1,18-.1,9-.1,18+.1),
locate(3,-6,"(3,-6)"),locate(5,2,"(5,2)"),locate(7,10,"(7,10)"),locate(9,18,"(9,18)")




)}}} 

They look like they do, judging from the above. We draw a
line through them:

{{{drawing(278.6,600,-2,11,-8,20, graph(278.6,600,-2,11,-8,20,0,4x-18), 

line(3+.1,-6,3-.1,-6),line(3,-6+.1,3,-6-.1),line(3+.1,-6+.1,3-.1,-6),line(3+.1,-6-.1,3-.1,-6+.1),
line(5+.1,2,5-.1,2),line(5,2+.1,5,2-.1),line(5+.1,2+.1,5-.1,2-.1),line(5+.1,2-.1,5-.1,2+.1),
line(7+.1,10,7-.1,10),line(7,10+.1,7,10-.1),line(7+.1,10+.1,7-.1,10-.1),line(7+.1,10-.1,7-.1,10+.1),
line(9+.1,18,9-.1,18),line(9,18+.1,9,18-.1),line(9+.1,18+.1,9-.1,18-.1),line(9+.1,18-.1,9-.1,18+.1),
locate(3,-6,"(3,-6)"),locate(5,2,"(5,2)"),locate(7,10,"(7,10)"),locate(9,18,"(9,18)")

)}}} 

We can pick any two points of the four points 
to find the slope of the line.  We'll get the
same slope no matter which two of the points
we pick.  Let's pick (5,2) and {9,18).

To find the slope we use the slope formula:

{{{m=(y[2]-y[1])/(x[2]-x[1])}}}

where {{{x[1]=5}}}, {{{y[1]=2}}}, {{{x[2]=9}}}, {{{y[2]=18}}}

{{{m=(y[2]-y[1])/(x[2]-x[1])=(18-2)/(9-5)=16/4=4}}}

To find the equation, we use the point slope form:

{{{y-y[1]=m(x-x[1])}}}

{{{y-2=4(x-5)}}}

and we solve for y and simplify to get the 

slope intercept form:

{{{y-2=4x-20}}}

{{{y=4x-18}}}

Edwin</pre>