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

Answer:[tex]2x - 5y = 7\:\:or\:\:y = \frac{2}{5}x - 1\frac{2}{5}[/tex]Step-by-step explanation:First, find the rate of change [slope]:[tex]\frac{-y_1 + y_2}{-x_1 + x_2} = m[/tex][tex]\frac{3 + 1}{4 + 6} = \frac{4}{10} = \frac{2}{5}[/tex]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 = by = 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 = by = 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.