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Which equation represents the line that passes through the points (2,7) and (1, 5)?

User Nirg
by
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1 Answer

5 votes

Explanation:

in what form (or format) do you need that equation ?

there are e.g. the slope-intercept form and the point-slope forms.

y = ax + b

is the slope intercept form ("a" is the slope, "b" is the y-intercept).

y - y1 = a(x - x1)

is the point-slope form ("a" is again the slope, x1,y1 are the coordinates of one point on the line).

they have the slope in common.

the slope of a line is the ratio

y coordinate difference / x coordinate difference

when gong from one point on the line to another.

we are given 2 points, so the point-slope form is the easiest to start with.

first the slope :

when going from (2, 7) to (1, 5)

x changes by -1 (from 2 to 1).

y changes by -2 (from 7 to 5).

the slope "a" is -2/-1 = 2.

and then I pick the point (1, 5), simply because it has the smaller numbers :

y - 5 = 2(x - 1)

that's the point-slope form.

to get the slope-intercept form, we only need make a simple transformation :

y - 5 = 2(x - 1) = 2x - 2

y = 2x + 3

that's it.

User Niklesh Raut
by
8.2k points

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