SOLUTION: What is the equation of the line passing through the points(3,7) and (11,13)?
Also explain to me what is slope?
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Question 178918: What is the equation of the line passing through the points(3,7) and (11,13)?
Also explain to me what is slope?
Found 2 solutions by Mathtut, ankor@dixie-net.com:
Answer by Mathtut(3670) (Show Source): You can put this solution on YOUR website!
3,7) and (11,13)?
slope is the change in y values divided by the change in the x values of 2 points on a line. It is a measurement of how fast or slow a line rises or falls.
Rise would be a positive slope and when a slope falls it is negative.
When looking at a line slope of the line is is considered positive and rising if ascends, from left to right. When looking at a line the slope of the line is considered negative and falling, if it descends looking from left to right.
:
m=slope==change in y/change in x=rise/run.
:
lets call (3,7) (x1,y1) and (11,13) (x2,y2)
:
you can take the slope from either point but cannot change direction in the middle. In other words you can have y1-y2/x1-x2 or y2-y2/x2-x1 but you cannot have y2-y1/x1-x2 or y1-y2/x2-x1. You must remain consistent through the change in y over change in x
:
m=(13-7)/(11-3)=6/8=3/4
:
so slope is 3/4 for these 2 points
:
now we use the point slope formula....we can use either point and of course the slope is 3/4
:
y-k=m(x-h) where (h,k) is any point on the line and m is the slope
:
I will use (3,7) as my point
:
y-7=(3/4)(x-3)
:
y-7=(3/4)x-9/4
:
y=(3/4)x+19/4 or we could write this as 4y=3x-9-->3x-4y=9(multiplied terms by 4)
:
:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
One definition or slope is "rise over run", a good way to think of it:
The algebra formula for slope (m): m =
It says the same thing, y is vertical component, (rise) x is the horizontal (run)
:
What is the equation of the line passing through the points(3,7) and (11,13)?
:
In this problem we can sign the given coordinates as follows to find the slope
x1=3, y1=7
x2=11,y2=13
:
m = = reduces to is the slope
:
Use the point/slope formula to create the equation: y-y1 = m(x-x1)
y - 7 = (x - 3)
:
y - 7 = x - *3
:
y - 7 = x -
:
y = x - + 7
:
y = x - +
:
y = x + ; is the equation for this line
:
:
Check this by substituting the x value and ensuring that it agrees with the y value
for example using the 3, 7
y = (3) +
y = +
y = which = 7
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