What is an equation in slope intercept form of the line that passes through (6, 10) and is parallel to the graph of y=1/3x-1

Given:The equation of line is[tex]y=\dfrac{1}{3}x-1[/tex]To find:The equation of line in slope-intercept form parallel to given line and passes through (6,10).Solution:The slope intercept form of a line is[tex]y=mx+b[/tex]       ...(i)where, m is slope and b is y-intercept.The equation of given line is[tex]y=\dfrac{1}{3}x-1[/tex]          ...(ii)On comparing (i) and (ii), we get[tex]m=\dfrac{1}{3}[/tex]Slope of given line is [tex]\dfrac{1}{3}[/tex].We know that slope of parallel lines are same. So, the slope of required line is [tex]\dfrac{1}{3}[/tex].Since slope of required line is [tex]\dfrac{1}{3}[/tex] and it passes through (6,10), therefore the equation of line is[tex]y-y_1=m(x-x_1)[/tex][tex]y-10=\dfrac{1}{3}(x-6)[/tex][tex]y-10=\dfrac{1}{3}(x)-\dfrac{1}{3}(6)[/tex][tex]y-10=\dfrac{1}{3}(x)-2[/tex]Add 10 on both sides.[tex]y-10+10=\dfrac{1}{3}(x)-2+10[/tex][tex]y=\dfrac{1}{3}(x)+8[/tex]Therefore, the required equation of line is [tex]y=\dfrac{1}{3}(x)+8[/tex].