SOLUTION: a ine passes through (3,4)and(4,7) write an equation for the line in point slope form rewrite the equation in standard form using integers

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Question 392668: a ine passes through (3,4)and(4,7)
write an equation for the line in point slope form
rewrite the equation in standard form using integers
Found 3 solutions by Alan3354, nerdybill, ewatrrr:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Given 2 points example.
Find the equation of the line thru the points (2,1) and (3,5)
---------------------
This is a 2 step process. First find the slope of the line thru the points.
slope, m = diffy/diffx
m = (5-1)/(3-2)
m = 4
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Now use y = mx + b with either point to find b, the y-intercept.
y = mx + b
5 = 4*3 + b
b = -7
-------
y = mx + b
y = 4x - 7 is the answer.
------------------------
Another approach using determinants:
|x y 1|
|2 1 1| = 0
|3 5 1|
--------
x(1-5) - y(2-3) + 1(10-3) = 0
-4x + y + 7 = 0
y = 4x - 7
---------
For further assistance, or to check your work, email me via the thank you note
or at Moral Loophole@aol.com
Answer by nerdybill(7384)   (Show Source): You can put this solution on YOUR website!
First, determine slope of:
(3,4)and(4,7)
m = (y2-y1)/(x2-x1)
m = (7-4)/(4-3)
m = (3)/(1)
m = 1
.
Using the slope above and one of the two points (3,4) and plug it into the "point-slope" form:
y - y1 = m(x - x1)
y - 4 = 1(x - 3)
y - 4 = x - 3
y = x + 1 (equation of line in "slope-intercept" form)
.
standard form:
y = x + 1
-x + y = 1
x - y = 1




Answer by ewatrrr(24785)   (Show Source): You can put this solution on YOUR website!


Hi

Using the point-slope formula, 

(3,4)and

(4,7)    m = 4-7 /3-4  = -3/-1 = 3

m = 3

 the standard slope-intercept form for an equation of a line y = mx + b  

where m is the slope and b the y-intercept.  

y = 3x + b   |using ordered pair Pt(3,4) to solve for b

4 = 3*3 + b

-5 = b

y = 3x - 5

Standard form

 3x-y = 5 

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