Determine the equation of a straight line passing through (3,-1) and parallel to 2y-6x=1
easiest way:
since it is parallel it must differ only in the constant
let the equation be
2y - 6x = x
at (3,-1)
-2 - 18 = c
c = -20
2y - 6x = -20
or
3x - y = 10
(3,-1).
-6x + 2y = 1
Parallel lines have equal slopes:
m1 = m2 = -A/B = 6/-2 = -3
Y = mx + b = -1
-3*3 + b = -1
b = 8
Eq: Y = -3x + 8
CORRECTION:
m1 = m2 = -A/B = 6/2 = 3
Y = mx + b = -1
3*3 + b = -1
b = -10
Eq: Y = 3x - 10
lebo
To determine the equation of a straight line parallel to a given line, we need to find the slope of the given line and then use that slope to find the equation of the parallel line passing through the given point.
First, let's rewrite the given line in slope-intercept form (y = mx + b), where m represents the slope and b is the y-intercept. Given line: 2y - 6x = 1
Rearranging the equation, we get: 2y = 6x + 1
Divide both sides by 2: y = 3x + 1/2
From this equation, we can see that the slope of the given line is 3.
Since the line we are looking for is parallel to the given line, it will have the same slope. Therefore, the slope of the line we want is also 3.
Now that we have the slope (m = 3) and a point (3, -1) that the line passes through, we can use the point-slope form of the equation of a line: y - y1 = m(x - x1), where (x1, y1) is the given point.
Plugging in the values, we get: y - (-1) = 3(x - 3)
Simplifying further, we have: y + 1 = 3(x - 3)
Expanding the right side, we get: y + 1 = 3x - 9
To obtain the final equation of the line, we isolate y by subtracting 1 from both sides: y = 3x - 10
Therefore, the equation of the straight line passing through (3, -1) and parallel to 2y - 6x = 1 is y = 3x - 10.