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[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Question:-}}}}\diamond[/tex]
Find the equation of a line parallel to y-5=6x-10 that passes through (4,10)
[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Answer and how to solve:-}}}}\diamond[/tex]
❖ If lines are parallel to each other, they have the same slope.
So the slope of the line parallel to y-5=6x-10 is 6.
Now, since we're also given the point crossed by the line, we write the equation in point-slope form:-
[tex]\sf{y-y_1=m(x-x_1)}[/tex]
Substitute 10 for y₁, 6 for m and 4 for x₁:-
[tex]\sf{y-10=6(x-4)}[/tex]
On simplification,
[tex]\sf{y-10=6x-24}[/tex]
Adding 10 to both sides results in:-
[tex]\sf{y=6x-14}[/tex]
So we conclude that Option A is correct.
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