Write the equation of the line that passes through (−3, 5) and (2, 10) in slope-intercept form.

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].