Can't someone please help me with these equations.
State whether the lines are parallel, perpendicular, or neither.
16. -14x = -632 - 26y
y = (7/13)x - 316/13
18. x + 6y = 196
689 = (6201/230)y + (4823/460)x
I would really apreciate your help.
arrange the equations into the form
ax + by = c
1. -14x = -632 - 26y ---> 14x - 26y = 632
slope = 14/26 = 7/13
y = (7/13)x - 316/13 ---> 7x - 13y = 316
slope = -7/-13 = 7/13
since the slopes are equal, they must be parallel.
To be perpendicular, their slopes must be opposite reciprocals of each other.
try the second one.
Sure! I can help you with these equations. Let's analyze each pair of equations to determine whether the lines are parallel, perpendicular, or neither.
16.
Equation 1: -14x = -632 - 26y
Equation 2: y = (7/13)x - 316/13
To determine the relationship between the lines described by these equations, we need to compare their slopes. The slope-intercept form of Equation 2 (y = mx + b) shows that the slope is (7/13).
In Equation 1, we can rewrite it as -26y = -14x - 632 and then simplify it to y = (14/26)x + (632/26), which simplifies further to y = (7/13)x + (316/13). Notice that the slope is also (7/13) in Equation 1.
Since the slopes of both equations are the same, the lines are parallel.
18.
Equation 1: x + 6y = 196
Equation 2: 689 = (6201/230)y + (4823/460)x
To identify the relationship between the lines described by these equations, we need to compare their slopes. We can rewrite Equation 2 in slope-intercept form by rearranging the terms:
Equation 2: (4823/460)x + (6201/230)y = 689
Dividing all terms by their common denominators:
4x + 27y = 298
Comparing this equation to Equation 1, we observe that the coefficients of x and y are not proportional. This means that the slopes of the two lines are not equal.
Since the slopes are not equal, the lines described by these equations are neither parallel nor perpendicular.
I hope this clarifies the relationship between the lines in each of the given equations. Let me know if you have any further questions!
Of course, I'd be happy to help you with these equations and determine whether the lines are parallel, perpendicular, or neither. Let's start by analyzing each pair of equations.
16. We have two equations:
Equation 1: -14x = -632 - 26y
Equation 2: y = (7/13)x - 316/13
To determine if these lines are parallel, perpendicular, or neither, we need to compare their slopes. The slope-intercept form of a linear equation is y = mx + b, where 'm' represents the slope of the line.
For Equation 1: -14x = -632 - 26y
To determine its slope, rearrange the equation to slope-intercept form: -26y = -14x - 632, then divide all terms by -26:
y = (14/26)x + 632/26 simplified to y = (7/13)x + 316/13.
Comparing the slopes, we see that the slope of Equation 2 is (7/13), which is also the slope of Equation 1. Since the slopes are equal, the lines represented by these equations are parallel.
18. The two equations are:
Equation 1: x + 6y = 196
Equation 2: 689 = (6201/230)y + (4823/460)x
Again, we need to compare slopes to determine whether these lines are parallel, perpendicular, or neither.
For Equation 1: x + 6y = 196
Rearrange the equation to slope-intercept form: 6y = -x + 196, and then divide all terms by 6:
y = (-1/6)x + 196/6 simplified to y = (-1/6)x + 98/3.
For Equation 2: 689 = (6201/230)y + (4823/460)x
Rearrange the equation to slope-intercept form by isolating the y-term:
(6201/230)y = 689 - (4823/460)x, then divide all terms by (6201/230) to solve for y:
y = [(689 - (4823/460)x) * (230/6201)].
Comparing the slopes, we have (-1/6) for Equation 1 and [(689 - (4823/460)x) * (230/6201)] for Equation 2. Since the slopes are not equal, the lines represented by these equations are neither parallel nor perpendicular.
To summarize:
16. The lines represented by equations -14x = -632 - 26y and y = (7/13)x - 316/13 are parallel.
18. The lines represented by equations x + 6y = 196 and 689 = (6201/230)y + (4823/460)x are neither parallel nor perpendicular.
I hope this explanation helps you understand how to determine the relationship between lines given their equations. Let me know if you have any more questions!