Answer:
2x - y = 7
Step-by-step explanation:
Parallel lines have the same slope and the equation will have the same form
That is
2x - y = c ← c will have different values depending on the point it passes through.
Here the line passes through (3, - 1 ) , thus substituting into the left side
2(3) - (- 1) = 6 + 1 = 7 ← value of c, hence
2x - y = 7 ← equation of line
The line's equation is y = 2x - 7.
In geometry, the coplanar straight lines that do not intersect at any point are called parallel lines. The slopes of parallel lines are equal because they are equally inclined with the positive x-axis.
The equation of the given line is
2x-y = 6
i.e. y = 2x-6
We know that If the equation of a line can be expressed as y = mx+c, then the slope of this line is m.
So, the slope of this given line is 2.
We can assume that the equation of the line which is parallel to the given line can be written as
y = 2x + c ...(1)
, where c is a constant.
Since this line passes through the point (3, -1), you have to put x = 3 and y = -1 in (1), to get the value of the constant.
Now, c = y - 2x = (-1) - 2*3 = (-1) - 6 = -7
Putting this value in (1), we get
y = 2x - 7
Therefore the required equation of the line is y = 2x - 7.
Know more about parallel lines here -
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