Equation of a line is expressed as:
y = mx+c where;
m is the slope of the line
c is the intercept
Given the coordinates (-2, 3) and (1,5)
Get the slope first
m = y2-y1/x2-x1
From the coordinates
x1 = -2, y1 = 3, x2 = 1 and y2 = 5
m = 5-3/1-(-2)
m = 2/3
Next is to get the intercept c. To do that you will have to substitute any of the point into the formula y = mx+c
Using the coordinate (1,5) and m = 2/3
5 = 2/3(1) + c
5 = 2/3 + c
c = 5 - 2/3
c = (15-2)/3
c = 13/3
Finally substitute m = 2/3 and c = 13/3 into the equation y = mx+c to get the required equation:
y = 2/3 x + 13/3
multiply through by 3
3y = 2x + 13
3y-2x = 13
Hence the required equation of the line is 3y-2x = 13