Find equation of a line parallel to line with an equation y = 5x + 1 and passing through (1, 10).

The correct answer is: Equation of the given line is 5x - y = -5.

Step-by-step solution:-
Let l be the line for which slope is to be found.
Comparing the equation y = 5x + 1 with standard form of a straight line i.e. y = mx + c, we get-
m = 5 …...................................................................................................... (Equation i)
Now, line l is parallel to this line (y = 5x + 1) ......................................... (Given)
and we know that- Slopes of parallel lines are equal.
∴ Slope of line l = slope of line (y = 5x + 1)
∴ Slope of line l = 5 ....................... (From Equation i) ............................ (Equation ii)
We are given that line l passes through the point (1,10) and we know its slope.
i.e. x1 = 1 & y1 = 10 & m = 5
We can use slope point form of an equation to find the equation of line l-
(y - y1) = m (x-x1)
∴ (y - 10) = 5 (x-1)
∴ y - 10 = 5x - 5
∴ -10 + 5 = 5x - y
∴ -5 = 5x - y
i.e. 5x - y = -5
Final Answer:-
∴ Equation of the given line is 5x - y = -5.