Answer:
[tex]3y+7x=-5[/tex] is the required equation.
Step-by-step explanation:
We have been given two points: (-2,3) and (1,-4)
We have a formula to find the equation with two points:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}\cdot (x-x_1)[/tex]
Here, we have:
[tex]x_1=-2,x_2=1,y_1=3,y_2=-4[/tex]
On substituting the values in the formula we get:
[tex]y-3=\frac{-4-3}{1-(-2)}\cdot (x-(-2))[/tex]
[tex]\Rightarrow y-3=\frac{-7}{3}\cdot (x+2)[/tex]
On further simplification:
[tex]3y-9=-7(x+2)[/tex]
[tex]\Rightarrow 3y-9=-7x-14[/tex]
After rearranging the terms
[tex]3y+7x=-14+9[/tex]
After final simplification we get:
[tex]3y+7x=-5[/tex]
