Step-by-step explanation:
A line can be repsented by slope-intercept form:
[tex]y = mx + b[/tex]
where [tex]m[/tex] is the slope of the line and [tex]b[/tex] is the y-intercept.
The slope of the line is represented by the change in the [tex]y[/tex] values on the line divided by the change in the [tex]x[/tex] values on the line, or, simply put,
[tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]
for any two points [tex](x_{1}, y_{1})[/tex] and [tex](x_{2}, y_{2})[/tex] that are on the line.
Taking any two points on the given line, we can see that the slope of the above graph is [tex]1[/tex], so we can plug this in for [tex]m[/tex]:
[tex]y = x + b[/tex]
This eliminates options C and D.
Now, the y-intercept is the point at which the line crosses the y-axis, or, simply put, what the value of the line is at [tex]x = 0[/tex].
Looking at the line, it crosses the y-axis at [tex](0, 6)[/tex], meaning we can plug in [tex]6[/tex] for [tex]b[/tex] in our equation and get our answer:
[tex]y = x + 6[/tex]
