Question

Find an equation for the line that passes through the points(-4,-3)and(6,1).

Answer 1

`2x - 5y = 7\:\:or\:\:y = (2)/(5)x - 1(2)/(5)`

Explanation:

First, find the rate of change [slope]:

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

`(3 + 1)/(4 + 6) = (4)/(10) = (2)/(5)`

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:

1 = ⅖[6] + b

2⅖

−1⅖ = b

y = ⅖x - 1⅖ >> Line in Slope-Intercept Form

If you need it written in Standard Form:

y = ⅖x - 1⅖

-⅖x -⅖x

_________

−⅖x + y = −1⅖ [We do not want fractions in our standard equation, so multiply by the denominator to get rid of it.]

−5[−⅖x + y = −1⅖]

2x - 5y = 7 >> Line in Standard Form

_______________________________________________

−3 = ⅖[−4] + b

−1⅗

−1⅖ = b

y = ⅖x - 1⅖ >> Line in Slope-Intercept Form

If you need it written in Standard Form:

y = ⅖x - 1⅖

-⅖x -⅖x

_________

−⅖x + y = −1⅖ [We do not want fractions in our standard equation, so multiply by the denominator to get rid of it.]

−5[−⅖x + y = −1⅖]

2x - 5y = 7 >> Line in Standard Form

** 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.