y = 6x + 2 is the equation of the line that passes through the point (1,8) and is parallel to the line 6x - y = 5
Solution:
Given that, we have to write the equation of the line that passes through the point (1,8) and is parallel to the line 6x - y = 5
The equation of line in slope intercept form is given as:
y = mx + c --------- eqn 1
Given equation of line:
6x - y = 5
y = 6x - 5
On comparing the above equation with eqn 1,
m = 6
We know that slopes of parallel lines are equal
Therefore, slope of line parallel to given line is also 6
Now find the equation of line with slope 6 and passes through point (1, 8)
Substitute m = 6 and (x, y) = (1, 8) in eqn 1
8 = 6(1) + c
c = 2
Substitute c = 2 and m = 6 in eqn 1
y = 6x + 2
Thus equation of line is found