find the pair own parallel lines
1)-12y+15x=-4
2)4y=-5x-4
3)15+12y=-4
1) -12y + 15x = -4 ---> 5x - 4y = -4/3
2) 4y = 5x - 4 ---> 5x - 4y = 4 , mmmmhhhhh
3) 15 + 12y = -4 , clearly out, since it has no x term
To determine if two lines are parallel, we need to compare their equations and observe the relationship between the coefficients of the variables.
Let's consider the given equations:
1) -12y + 15x = -4
2) 4y = -5x - 4
3) 15 + 12y = -4
First, we need to rewrite the equations in the form y = mx + c, where m represents the slope.
1) -12y + 15x = -4 -> -12y = -15x - 4 -> y = 5/4x + 1/3
2) 4y = -5x - 4 -> y = -5/4x - 1
3) 15 + 12y = -4 -> 12y = -19 -> y = -19/12
Now that we have the equations in the slope-intercept form, we can compare the slopes (m) of the lines.
The slopes for the given equations are:
1) m1 = 5/4
2) m2 = -5/4
3) m3 = 0
For two lines to be parallel, their slopes must be equal.
By comparing the slopes of the equations, we can determine that:
- Equations 1) and 2) have slopes of -5/4 and 5/4 respectively, which are negative reciprocals of each other. Therefore, equations 1) and 2) are parallel.
- Equation 3) has a slope of 0, which is different from the slopes of equations 1) and 2). Therefore, equation 3) is not parallel to either of the other equations.
In summary:
The pair of parallel lines are equations 1) and 2) from the given set.