Question

What is the equation of the line passing through the points (-2,3) and (1,4)?

Answer 1

Given the points below;

`\left(-2,3\right)\text{ }and\text{ }(1,4)`

To find the equation of a straight line, the formula is

`(y-y_1)/(x-x_1)=(y_2-y_1)/(x_2-x_1)`

Where

`\begin{gathered} (x_1,y_1)=(-2,3) \\ (x_2,y_2)=(1,4) \end{gathered}`

Substitute the values of the coordinates into the formula to find the equation of a straight line above

`\begin{gathered} (y-y_(1))/(x-x_(1))=(y_(2)-y_(1))/(x_(2)-x_(1)) \\ (y-3)/(x-(-2))=(4-3)/(1-(-2)) \\ (y-3)/(x+2)=(1)/(1+2) \\ (y-3)/(x+2)=(1)/(3) \\ Crossmultiply \\ 3(y-3)=1(x+2) \\ 3y-9=x+2 \\ x+2=3y-9 \\ x+2-(3y-9)=0 \\ x+2-3y+9=0 \\ x-3y+2+9=0 \\ x-3y+11=0 \end{gathered}`

Hence, the general equation of the line is

`x-3y+11=0`