Maths-
General
Easy
Question
Find equation of a line parallel to line with an equation y = 5x + 1 and passing through (1, 10).
The correct answer is: 5x - y = - 5.
Hint:-
1. The slope of a line can be defined as the change in y coordinates of any 2 points on that line corresponding to the change in the x coordinates of those 2 points. This is generally referred to as the rise to run ratio of the given line i.e. how much did the y-coordinates rise vis-a-vis how long a distance was covered by the x-coordinates. Slope = m = rise / run = y2-y1 / x2-x1
2. Parallel lines have equal slopes.
3. Equation of a line in slope point form is-
(y-y1) = m (x-x1)
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.
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