Write the equation in slope-intercept form of a line that has a slope of One-third and passes through the point (-6, 0).
y = one-third x
y = one-third x minus 6
y = one-third x minus 2
y = one-third x + 2

The equation in slope-intercept form is y = 1/3x  + 2

The equation of the line in point slope form is expressed as:

where:

Substitute:

y - 0 = 1/3(x+6)

Write in slope-intercept form

y = 1/3(x+6)

3y = x + 6

y = 1/3x + 6/3

y = 1/3x + 2

Hence the equation in slope-intercept form is y = 1/3x  + 2

Learn more on slope-intercept here: link

Slope-intercept form:  y = mx + b

(m is the slope, b is the y-intercept or the y value when x = 0 --> (0, y) or the point where the line crosses through the y-axis)

You know:

m =      So substitute/plug it into the equation

y = mx + b

  To find b, plug in the point (-6, 0) into the equation, the isolate/get the variable "b" by itself

0 = -2 + b         Add 2 on both sides to get "b" by itself

0 + 2 = -2 + 2 + b

2 = b

      Your answer is the 4th option