you can do it by yourself...first of all find the point of intersection of any two lines by using elimination method (or any other u like) then drop a perpendicular from this point to the opposite side now u know that this is the altitude and the slope of altitude can be find using the equation of the line on which it is perpendicular.... now use the point-slope form of line I.e, (y-y1)=m(x-x1)...

Equation of Altitudes:
To find the equation of the altitudes of a triangle, we need to first find the slopes of the corresponding sides. The slopes of the altitudes are negative reciprocals of the slopes of the sides.

Given triangle sides:
1) 3x - 2y = 6
2) 3x + 4y = 12
3) 3x - 8y = 12

Slope of Side 1:
To find the slope of side 1, we need to rewrite the equation in the slope-intercept form (y = mx + c).

3x - 2y = 6
-2y = -3x + 6
y = (3/2)x - 3

The slope of side 1 is 3/2.

Equation of Altitude 1:
The slope of the altitude corresponding to side 1 is the negative reciprocal of 3/2, which is -2/3.

Using the point-slope form (y - y1 = m(x - x1)), we can find the equation of the altitude passing through a given point on side 1.

Let's take the point (0, -3) on side 1.

y - (-3) = (-2/3)(x - 0)
y + 3 = (-2/3)x
3y + 9 = -2x
2x + 3y + 9 = 0

Therefore, the equation of altitude 1 is 2x + 3y + 9 = 0.

Slope of Side 2:
To find the slope of side 2, we need to rewrite the equation in the slope-intercept form.

3x + 4y = 12
4y = -3x + 12
y = (-3/4)x + 3

The slope of side 2 is -3/4.

Equation of Altitude 2:
The slope of the altitude corresponding to side 2 is the negative reciprocal of -3/4, which is 4/3.

Using the point-slope form, let's take the point (0, 3) on side 2.

y - 3 = (4/3)(x - 0)
y - 3 = (4/3)x
3y - 9 = 4x
4x - 3y + 9 = 0

Therefore, the equation of altitude 2 is 4x - 3y + 9 = 0.

Slope of Side 3:
To find the slope of side 3, we need to rewrite the equation in the slope-intercept form.

3x - 8y = 12
-8y = -3x + 12
y = (3/8)x - 3/2

The slope of side 3 is 3/8.

Equation of Altitude 3:
The slope of the altitude corresponding to side 3 is the negative reciprocal of 3/8, which is -8/3.

Using the point-slope form, let's take the point (0, -3/2) on side 3.

y - (-3/2)