Question 147601
First let's find the equation of the line with a slope of 3 which goes through the point (1,4)



If you want to find the equation of line with a given a slope of {{{3}}} which goes through the point (1,4), 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-4=(3)(x-1)}}} Plug in {{{m=3}}}, {{{x[1]=1}}}, and {{{y[1]=4}}} (these values are given)



{{{y-4=3x+(3)(-1)}}} Distribute {{{3}}}


{{{y-4=3x-3}}} Multiply {{{3}}} and {{{-1}}} to get {{{-3}}}


{{{y=3x-3+4}}} Add 4 to  both sides to isolate y


{{{y=3x+1}}} Combine like terms {{{-3}}} and {{{4}}} to get {{{1}}} 

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Answer:



So the equation of the line with a slope of {{{3}}} which goes through the point (1,4) is {{{y=3x+1}}} 




Notice how choice D) has the same x-coordinate as the given point. Since one x-value can <font size=4><b>only</b></font> generate one y-value, this means that we can eliminate choice D)



Now also notice how the rest of the choices have an x-coordinate of 4. So let's plug in {{{x=4}}} to find y



{{{y=3x+1}}} Start with the given equation.



{{{y=3(4)+1}}} Plug in {{{x=4}}}.



{{{y=12+1}}} Multiply {{{3}}} and {{{4}}} to get {{{12}}}.



{{{y=13}}} Combine like terms.



Since <font size=4><b>none</b></font> of the choices have  a y-coordinate of 13, this means that <font size=4><b>none</b></font> of the choices are correct. So I would double check the problem.