Question

What is an equation of the line that passes through the points (1,3) and (8,5)

Answer 1

`2x - 7y = -19\:or\:y = (2)/(7)x + 2(5)/(7)`

Explanation:

First, find the rate of change [slope]:

`(-y_1 + y_2)/(-x_1 + x_2) = m`

`(-3 + 5)/(-1 + 8) = (2)/(7)`

Then plug these coordinates into the Slope-Intercept Formula instead of the Point-Slope Formula because you get it done much swiftly. It does not matter which ordered pair you choose:

5 = 2⁄7[8] + b

2 2⁄7

`2(5)/(7) = b \\ \\ y = (2)/(7)x + 2(5)/(7)`

If you want it in Standard Form:

y = 2⁄7x + 2 5⁄7

- 2⁄7x - 2⁄7x

________________

−2⁄7x + y = 2 5⁄7 [We do not want fractions in our Standard Equation, so multiply by the denominator to get rid of it.]

−7[−2⁄7x + y = 2 5⁄7]

`2x - 7y = -19`

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3 = 2⁄7 + b

`2(5)/(7) = b \\ \\ y = (2)/(7)x + 2(5)/(7)`

y = 2⁄7x + 2 5⁄7

- 2⁄7x - 2⁄7x

_______________

−2⁄7x + y = 2 5⁄7 [We do not want fractions in our Standard Equation, so multiply by the denominator to get rid of it.]

−7[−2⁄7x + y = 2 5⁄7]

`2x - 7y = -19`

** You see? I told you it did not matter which ordered pair you choose because you will always get the exact same result.

I am joyous to assist you anytime.