Question

what is the equation of the line that goes through (-3,-1) and (3,3) A. 3x+2y=15B. 3y+2x=15C. 3x-2y=3D. 2x-3y=-3

Answer 1

We are to find the equation of the line that goes through (-3,-1) and (3,3)

`\begin{gathered} (y-y_1)/(x-x_1)\text{ = }(y_2-y_1)/(x_2-x_1) \\ \\ x_1=-3,x_2=3,y_1=-1andy_2=3_{} \\ \\ \frac{y-(-1)_{}}{x-(-3)_{}}\text{ = }\frac{3_{}-(-1)_{}}{3_{}-(-3)_{}} \\ \\ \frac{y\text{ + 1}}{x\text{ + 3}}\text{ = }\frac{3\text{ + 1}}{3\text{ + 3}} \\ \\ \frac{y\text{ + 1}}{x\text{ + 3}}\text{ = }(4)/(6) \\ \\ \frac{y\text{ + 1}}{x\text{ + 3}}\text{ = }(2)/(3) \end{gathered}`
`\begin{gathered} 3\text{ ( y + 1 ) = 2 ( x + 3 )} \\ 3y\text{ + 3 = 2x + 6} \\ 3y\text{ -2x = 6 - 3} \\ 3y\text{ - 2x = 3} \\ \end{gathered}`