Answer:
![2x - 5y = 7\:\:or\:\:y = \frac{2}{5}x - 1\frac{2}{5}](https://tex.z-dn.net/?f=2x%20-%205y%20%3D%207%5C%3A%5C%3Aor%5C%3A%5C%3Ay%20%3D%20%5Cfrac%7B2%7D%7B5%7Dx%20-%201%5Cfrac%7B2%7D%7B5%7D)
Step-by-step explanation:
First, find the <em>rate of</em><em> </em><em>change</em><em> </em>[<em>slope</em>]:
![\frac{-y_1 + y_2}{-x_1 + x_2} = m](https://tex.z-dn.net/?f=%5Cfrac%7B-y_1%20%2B%20y_2%7D%7B-x_1%20%2B%20x_2%7D%20%3D%20m)
![\frac{3 + 1}{4 + 6} = \frac{4}{10} = \frac{2}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B3%20%2B%201%7D%7B4%20%2B%206%7D%20%3D%20%5Cfrac%7B4%7D%7B10%7D%20%3D%20%5Cfrac%7B2%7D%7B5%7D)
Then plug these coordinates into the Slope-Intercept Formula instead of the <em>Point-Slope Formula</em> 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 <em>Slope-Intercept</em><em> </em><em>Form</em><em> </em>
If you need it written in <em>Standard Form</em>:
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 <em>Standard</em><em> </em><em>Form</em>
_______________________________________________
−3 = ⅖[−4] + b
−1⅗
−1⅖ = b
y = ⅖x - 1⅖ >> Line in <em>Slope-Intercept Form</em>
If you need it written in <em>Standard Form</em>:
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 <em>Standard</em><em> </em><em>Form</em>
** 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.