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Sagot :
Given the slope of the line:
[tex]m=-\frac{7}{12}[/tex]And this point on the line:
[tex](-6,12)[/tex](a) By definition, the Slope-Intercept Form of the equation of a line is:
[tex]y=mx+b[/tex]Where "m" is the slope and "b" is the y-intercept.
In this case, you can substitute the slope and the coordinates of the known point into that equation, and then solve for "b", in order to find the y-intercept:
[tex]12=(-\frac{7}{12})(-6)+b[/tex][tex]12=\frac{42}{12}+b[/tex][tex]\begin{gathered} 12=\frac{42}{12}+b \\ \\ 12=\frac{7}{2}+b \end{gathered}[/tex][tex]\begin{gathered} 12-\frac{7}{2}=b \\ \\ b=\frac{17}{2} \end{gathered}[/tex]Therefore, the equation of this line in Slope-Intercept Form is:
[tex]y=-\frac{7}{12}x+\frac{17}{2}[/tex](b) The Standard Form of the equation of a line is:
[tex]Ax+By=C[/tex]Where A, B, and C are integers, and A is positive.
In this case, you need to add this term to both sides of the equation found in Part (a), in order to rewrite it in Standard Form:
[tex]\frac{7}{12}x[/tex]Then, you get:
[tex]\frac{7}{12}x+y=\frac{17}{2}[/tex]Hence, the answers are:
(a) Slope-Intercept Form:
[tex]y=-\frac{7}{12}x+\frac{17}{2}[/tex](b) Standard Form:
[tex]\frac{7}{12}x+y=\frac{17}{2}[/tex]
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