I don’t understand how to solve these last three problems. Can someone please help me?
Determine whether the graphs of the given equations are parallel, perpendicular, or neither. (questions 6-8)
6.)
y = -2x + 3
2x + y = 7
A: Parallel
B: Perpendicular
C: Neither
7.)
y = -2x + 3
2x + y = 7
A: Parallel
B: Perpendicular
C: Neither
8.)
y = 4x - 2
-x + 4y = 0
A: Parallel
B: Perpendicular
C: Neither
the slopes of parallel lines are equal
the slopes of perpendicular lines multiply to give -1
6.) The slopes are -2 and -2
7.) The same problem!
8.) The slopes are 4 and 1/4
so, what do you think?
Oops!
7.)
y = x + 11
y = -x + 2
Thank You so much for your help Steve!
To determine whether the graphs of the given equations are parallel, perpendicular, or neither, you need to analyze the slopes of the equations.
Let's start with question 6:
Equation 1: y = -2x + 3
Equation 2: 2x + y = 7
To find the slope of Equation 1, identify the coefficient of x, which is -2. The slope of Equation 1 is -2.
To find the slope of Equation 2, rearrange it to the slope-intercept form (y = mx + b), where m is the slope.
2x + y = 7
y = -2x + 7
The coefficient next to x is -2, so the slope of Equation 2 is also -2.
Since the slopes of both equations are the same (-2), the graphs of these equations are parallel. Therefore, the answer for question 6 is A: Parallel.
Moving on to question 7:
Equation 1: y = -2x + 3
Equation 2: 2x + y = 7
Similarly, the slope of Equation 1 is -2.
To find the slope of Equation 2:
2x + y = 7
Subtract 2x from both sides:
y = -2x + 7
Again, the slope is -2.
Once again, the slopes of both equations are the same (-2), so the graphs of these equations are parallel. Therefore, the answer for question 7 is also A: Parallel.
Now let's move on to question 8:
Equation 1: y = 4x - 2
Equation 2: -x + 4y = 0
The slope of Equation 1 is 4.
To find the slope of Equation 2, rearrange it to make y the subject:
-x + 4y = 0
4y = x
y = (1/4)x
The coefficient next to x is 1/4, so the slope of Equation 2 is 1/4.
Since the slopes of the two equations are the negative reciprocals of each other (4 and 1/4), the graphs of these equations are perpendicular. Therefore, the answer for question 8 is B: Perpendicular.
By analyzing the slopes, you can determine whether the graphs of the equations are parallel, perpendicular, or neither.