Question 113988
If we have a y intercept of 3, then the line goes through (0,3)




If you want to find the equation of line with a given a slope of {{{1/2}}} which goes through the point ({{{0}}},{{{3}}}), you can simply use the point-slope formula to find the equation:



---Point-Slope Formula---
{{{y-y[1]=m(x-x[1])}}} where {{{m}}} is the slope, and *[Tex \Large \left(x_{1},y_{1}\right)] is the given point


So lets use the Point-Slope Formula to find the equation of the line


{{{y-3=(1/2)(x-0)}}} Plug in {{{m=1/2}}}, {{{x[1]=0}}}, and {{{y[1]=3}}} (these values are given)



{{{y-3=(1/2)x+(1/2)(-0)}}} Distribute {{{1/2}}}


{{{y-3=(1/2)x+0}}} Multiply {{{1/2}}} and {{{-0}}} to get {{{0}}}


{{{y=(1/2)x+0+3}}} Add 3 to  both sides to isolate y


{{{y=(1/2)x+3}}} Combine like terms {{{0}}} and {{{3}}} to get {{{3}}} 


Now let's convert {{{y=(1/2)x+3}}}  to standard form

*[invoke converting_linear_equations "slope-intercept_to_standard", 1, 2, 3, "1/2", 3]


So the answer is B)