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Linear equations

by Tammy
(New York)











































Can i see an example of the problem, (-18.9,17.2) and (-16.9,6.6)?

Comments for Linear equations

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Jul 23, 2011
Linear equations - Slope Intercept
by: Staff


The question:

Can i see an example of the problem, (-18.9,17.2) and (-16.9,6.6)?


The answer:

I’m not sure what question you want answered.

You did not ask a question.

I assume (1) the (-18.9,17.2) and (-16.9,6.6) are the x-y coordinates of two points, and (2) you would like to know the equation for a straight line passing thorough both points.



The equation for a straight line passing through two known points is shown below:


since you know the coordinates of the two points, you can calculate the slope (m)of the straight line which passes through both points as follows:

m = (y₂ - y₁)/(x₂ - x₁)


The slope-intercept form of an equation connecting the two points is:

y = mx + b

m = slope of line
b = y intercept

x & y are the x and y coordinates of any point on the straight line.

Once you know the slope of the line, you can solve for the y-intercept (b), and you are finished.



Your two points are: (-18.9,17.2) and (-16.9,6.6)


The slope of a straight line passing through both points is:

m = (y₂ - y₁)/(x₂ - x₁)
m = (6.6 - 17.2)/[(-16.9) - (-18.9)]
m = -10.6/2
m = -5.3

The equation for the straight line itself is:

y = mx + b
y = (-5.3)*x + b

Solve for “b” using the coordinates of either of the known points:

The coordinates of the first known point are: (-18.9,17.2)

y = (-5.3)*x + b

17.2 = (-5.3)*(-18.9) + b

17.2 = (-5.3)*(-18.9) + b

17.2 = 100.17 + b

17.2 - 100.17 = 100.17 - 100.17 + b

-82.97 = 0 + b

-82.97 = b



The final equation for the straight line is:

y = -5.3x - 82.97




check the equation by substituting the coordinates of both known points:

coordinates of the first point: (-18.9,17.2)

x = -18.9
y = 17.2

y = -5.3x - 82.97

y = (-5.3)*(-18.9) - 82.97

17.2 = 100.17 - 82.97

17.2 = 17.2, OK


coordinates of the second point: (-16.9,6.6)

x = -16.9
y = 6.6

y = -5.3x - 82.97

6.6 = (-5.3)*(- 16.9) - 82.97

6.6 = 89.57 - 82.97

6.6 = 6.6, OK




Thanks for writing.

Staff
www.solving-math-problems.com



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