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How To Find The Equation of a Line From a Graph | Algebra

User Msbyuva
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Explanation:

let's aim for the slope-inyercept form of the equation for a line :

y = ax + b

"a" is the slope of the line, "b" is the y-intercept (the y-value when x = 0).

the slope is the ratio

y coordinate difference / x coordinate difference

when going from one point on the line to another.

so, usually look for 2 points on the line in the graph that have "nice" (integer) coordinates. or any points where you can read the actual coordinates with very little error. or some points have been already specified for you with their actual coordinates.

P1 = (xp1, yp1)

P2 = (xp2, yp2)

the slope ("a") is simply

(yp2 - yp1)/(xp2 - xp1)

"b" is a mentioned the y-value for x = 0, so representing the point

(0, b)

if you cannot read that value very well on the graph, use the coordinates of one of the points P1 or P2 in the half-finished equation (e.g. for P1) :

yp1 = a×xp1 + b

b = yp1 - a×xp1 = yp1 - xp1(yp2 - yp1)/(xp2 - xp1)

or if you wanted to use P2

b = yp2 - a×xp2 = yp2 - xp2(yp2 - yp1)/(xp2 - xp1)

that's it.

User Sam Van Beastlo
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