I have to find the equation for the line that passes through (4,3) and (6,2) How would I solve this.

Into point slope form
Into slope intercept form

I got the slope each is -1/2
then I got y=-1/2x + b

How would I get b?

plug in one of the given points, then solve for b

e.g. using (4,3)

3 = (-1/2)(4) + b
etc.

(I get b=5)

ok

thank you again

To find the value of 'b' in the equation of the line, which is in the form of y = mx + b, you can use one of the points given to substitute the values of 'x' and 'y'. Let's use the point (4,3) for this example.

Start with the equation you derived:
y = (-1/2)x + b

Substitute the values of x and y from the point (4,3):
3 = (-1/2)(4) + b

Simplify and solve for 'b':
3 = -2 + b
b = 3 + 2
b = 5

Thus, the equation of the line passing through the points (4,3) and (6,2) can be written as y = (-1/2)x + 5.

Alternatively, you can also solve for 'b' at the beginning by using the slope of the line along with one of the given points. Since you already found the slope to be -1/2, you could use the point-slope form of the equation:

y - y1 = m(x - x1)

Using the point (4,3) as (x1, y1), substitute the values and simplify:

y - 3 = (-1/2)(x - 4)
y - 3 = (-1/2)x + 2
y = (-1/2)x + 5

So the result is the same; the equation of the line is y = (-1/2)x + 5.