Learn How To Find The Equation Of A Line Passing Through Any Two Distinct Points – Step-By-Step Guide Included

for any two distinct points

there is exactly one line containing them

I’ll assume that the question is incomplete and that the complete question is:

Find the equation of the line passing through any two distinct points.

To find the equation of a line passing through two distinct points, we can use the point-slope form of a linear equation:

y – y1 = m(x – x1)

where (x1, y1) are the coordinates of one of the two points, m is the slope of the line, and (x, y) are the coordinates of any other point on the line.

So, let’s say that we have two distinct points: (x1, y1) and (x2, y2). Then, the slope of the line passing through these two points is given by:

m = (y2 – y1) / (x2 – x1)

Substituting this value of m in the point-slope form, we get:

y – y1 = (y2 – y1) / (x2 – x1) (x – x1)

This is the equation of the line passing through the two distinct points (x1, y1) and (x2, y2).

We can also simplify this equation by multiplying both sides by (x2 – x1) to get it in the slope-intercept form:

y – y1 = (y2 – y1) / (x2 – x1) (x – x1)

y – y1 = mx – mx1 + y1

y = mx + (y1 – mx1)

where m = (y2 – y1) / (x2 – x1) is the slope of the line, and (y1 – mx1) is the y-intercept of the line.

So, the equation of the line passing through any two distinct points (x1, y1) and (x2, y2) is y = [(y2 – y1) / (x2 – x1)] x + [y1 – (y2 – y1) / (x2 – x1) x1].

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