If we were given two points on a linear equation

horrupavinvo

horrupavinvo

Answered question

2022-02-25

If we were given two points on a linear equation (x1,y1),(x2,y2), it is quite easy to find the slope and use substitution to find the slope intercept form y=mx+b, to graph it.
Is it possible to solve for b strictly in terms of x1,y1,x2,y2?

Answer & Explanation

cassidacc4

cassidacc4

Beginner2022-02-26Added 7 answers

Yes it is. As you say, we can find the slope:
m=y2y1x2x1
Thus,
y1=mx1+b=y2y1x2x1x1+b,
so
y1y2y1x2x1x1=x2y1x1y2x2x1=b.
besplodnexkj

besplodnexkj

Beginner2022-02-27Added 7 answers

Yes, by imposing that the three points (0,b),(x1,y1),(x2,y2) are aligned (determinant, or other way you know).

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