Answer: 2X + 3Y = 24 is Y = (-2/3)X + 3.
Explanation:
To find the equation of a line parallel to the line 2X+3Y=24 and passing through the point (3,1), we need to follow these steps:
1. First, let's rearrange the equation 2X+3Y=24 into slope-intercept form, which is Y = MX + B, where M is the slope and B is the y-intercept.
2X + 3Y = 24
3Y = -2X + 24
Y = (-2/3)X + 8
2. The given line has a slope of (-2/3). Since the line we want to find is parallel, it will have the same slope. Therefore, the equation of the line passing through (3,1) will also have a slope of (-2/3).
3. Next, we can use the point-slope form of a line to find the equation. The point-slope form is given by:
Y - Y1 = M(X - X1)
where (X1, Y1) is the given point (3,1), and M is the slope (-2/3).
4. Plugging in the values, we have:
Y - 1 = (-2/3)(X - 3)
5. Simplifying the equation further, we get:
Y - 1 = (-2/3)X + 2
6. To obtain the equation in slope-intercept form, we can isolate Y by adding 1 to both sides:
Y = (-2/3)X + 2 + 1
Y = (-2/3)X + 3
Therefore, the equation of the line that passes through the point (3,1) and is parallel to the line 2X + 3Y = 24 is Y = (-2/3)X + 3.