Question

What is the equation of a line given these two points: (2,3) and (-3, 4)

Answer 1

In order to find the equation of this line, let's use the slope-intercept form of the linear equation and the given points:

`\begin{gathered} y=mx+b \\ \\ (2,3)\colon \\ 3=2m+b \\ \\ (-3,4)\colon \\ 4=-3m+b\to b=4+3m \\ \\ 3=2m+(4+3m)_{}_{} \\ 3=5m+4 \\ 5m=3-4 \\ 5m=-1 \\ m=-(1)/(5) \\ \\ b=4+3(-(1)/(5)) \\ b=4-(3)/(5)=(20)/(5)-(3)/(5)=(17)/(5) \\ \\ y=-(1)/(5)x+(17)/(5) \end{gathered}`