Question

Write an equation of a line in slope intercept form that passes through (-5,4) and (9,-2)

Answer 1

The points are given as,

`\begin{gathered} (x_1,y_1)=(-5,4) \\ (x_2,y_2)=(9,-2) \end{gathered}`

The equation of a line in double point form is given as,

`\begin{gathered} (y-y_1)/(y_2-y_1)\text{ = }(x-x_1)/(x_2-x_1) \\ (y-4)/(-2-4)\text{ = }(x+5)/(9+5) \\ (y-4)/(-6)\text{ = }(x+5)/(14) \end{gathered}`

Simplifying further,

`\begin{gathered} 14(y-4)\text{ = -6\lparen x+5\rparen} \\ 14y\text{ - 56 = -6x -30} \\ 6x+14y\text{ = 56-30} \\ 6x\text{ + 14y = 26} \end{gathered}`

Converting the equation to slope-intercept form,slope-intercept

`\begin{gathered} 6x\text{ + 14y = 26} \\ 3x\text{ + 7y = 13} \\ 7y\text{ = -3x + 13} \\ y\text{ = }(-3x)/(7)+(13)/(7) \\ \end{gathered}`

Thus the required equation of line is,

`y=(-3x)/(7)\text{+}(13)/(7)`