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Find the equation of the line joining the points (1,6) and (6,1)

User Badrush
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1 Answer

5 votes

Explanation:

in what form do you need the equation ?

I assume it is the slope-intercept form :

y = ax + b

"a" being the slope of the line, "b" being the y-intercept of the line.

the slope of a line is the ratio

y-coordinate difference / x-coordinate difference

when going from one point on the line to another.

and the y-intercept (y-axis intercept, to be precise) is the y-value when x = 0.

so, starting with the slope, we go for example from (1, 6) to (6, 1) :

x changes by +5 (from 1 to 6).

y changes by -5 (from 6 to 1).

so, the slope is

-5/+5 = -1

so, we know, our equation looks like

y = -x + b

to get "b" we use one of the points, e.g. (1, 6) :

6 = -1 + b

b = 7

and our final equation is

y = -x + 7

User Robert Hyatt
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8.7k points

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