Find an equation of the line L in point slope form and in general form.
L is parallel to the line 3x-2y+5=0 and contains (2,3)
Given: 3x- 2y + 5 = 0, (2 , 3).
y = mx + b,
3 = (3/2)*2 + b,
3 = 3 + b,
b = o.
y = 3/2x,
2y = 3x,
-3x + 2y = 0,
3x - 2y = 0.
To find the equation of the line L in point-slope form and in general form, you need to determine the slope of the line and a point that lies on it.
Given that line L is parallel to the line 3x - 2y + 5 = 0, we can determine the slope of L by noting that parallel lines have the same slope. The given line can be rewritten in slope-intercept form as follows:
3x - 2y + 5 = 0
-2y = -3x - 5
y = (3/2)x + (5/2)
Thus, the slope of the given line is 3/2. Line L will also have a slope of 3/2.
Since line L contains the point (2, 3), we can now use the point-slope form of the equation of a line:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line and m is the slope of the line.
Substituting the coordinate values (x1, y1) = (2, 3) and the slope m = 3/2 into the equation, we get:
y - 3 = (3/2)(x - 2)
Multiplying through the parentheses, we have:
y - 3 = (3/2)x - 3
Adding 3 to both sides, we find:
y = (3/2)x
This is the equation of the line L in point-slope form.
To convert the point-slope form to the general form, we can rewrite it as:
(3/2)x - y = 0
Multiplying through by 2 to eliminate the fraction, we obtain:
3x - 2y = 0
Therefore, the equation of line L in general form is 3x - 2y = 0.