Question

The slope of a line is -1/3 and the y-intercept is 10/3. What is the equation of the line written in general form?

Answer 1

In slope-intercept form:
y = mx + b

where:
m = slope = -1/3
b = y-intercept = 10/3

y = (-1/3)x + 10/3

However, you want the equation organized in general form, which is:
Ax + By + C = 0

This simply requires us to rearrange terms (starting from slope-intercept form):
y = (-1/3)x + 10/3
(moving all terms to the left)
y - (-1/3)x - 10/3 = 0
y + 1/3x - 10/3 = 0

1/3x + y - 10/3 = 0

For general form:
A = 1/3
B = 1
C = -10/3

Answer 2

`Slope-intercept\ form:y=mx+b\\\\m-slpoe\\b-y-intercept\\\\y=-(1)/(3)x+(10)/(3)\\\\General\ form:Ax+By+C=0\\\\y=-(1)/(3)x+(10)/(3)\\\\(1)/(3)x+y-(10)/(3)=0\ \ \ \ /\cdot3\\\\x+3y-10=0`