Since slope-intercept form is y = mx + b where m is slope and b is the y-intercept, so to find what the equation of the line is, you need to find the values of both variables.
The equation for slope is (change in y)/(change in x), or y/x. You can set up the equation like this; [tex] m= \frac{y2-y1}{x2-x1}\\ m=\frac{10-5}{2-(-3)} \\ m=\frac{5}{2+3}\\ m=\frac{5}{5} m=1 [tex] So the slope of the line is 1.
To find the y-intercept, solve y = (1)x + b for b; [tex] y=x+b\\ b=y-x [tex] Plug the values of a point in for x and y; [tex] b=10-2\\ b=8 [tex]
This brings your final equation to be [tex] y=x+8 [tex].