Which equation represents a line that is parallel to the line whose equation is 3x - 2y = 7
A) Y= -3/2x + 5
B)Y= -2/3x + 4
C)Y= 3/2x - 5
D)Y= 2/3x - 4
I chose c
To determine which equation represents a line that is parallel to the line 3x - 2y = 7, we need to compare the slopes of the given options.
The given equation is in the form of y = mx + b, where m represents the slope.
Let's convert the given equation, 3x - 2y = 7, into slope-intercept form:
3x - 2y = 7
-2y = -3x + 7
y = (3/2)x - 7/2
We can see that the slope is (3/2).
Now, let's compare the slopes of the answer choices:
A) Y = -3/2x + 5 => The slope is -3/2, which is not equal to (3/2). This option is not parallel to the given line.
B) Y = -2/3x + 4 => The slope is -2/3, which is not equal to (3/2). This option is not parallel to the given line.
C) Y = 3/2x - 5 => The slope is 3/2, which is equal to (3/2). This option represents a line that is parallel to the given line.
D) Y = 2/3x - 4 => The slope is 2/3, which is not equal to (3/2). This option is not parallel to the given line.
Based on our analysis, you are correct. Option C) Y = 3/2x - 5 represents a line that is parallel to the line 3x - 2y = 7.
To determine which equation represents a line that is parallel to the line whose equation is 3x - 2y = 7, we need to analyze the slope of both lines.
The given equation is in the form of y = mx + b, where m represents the slope of the line. In this case, the slope can be found by rearranging the equation in y = mx + b form:
3x - 2y = 7
-2y = -3x + 7
Divide both sides by -2:
y = (3/2)x - 7/2
From the equation, we can see that the slope of the original line is 3/2.
To be parallel to this line, the slope of the new line must also be 3/2. Therefore, we need to look at the slopes of the given answer options.
Let's analyze option C) Y = 3/2x - 5:
The slope of this line is 3/2, which matches the slope of the original line. Therefore, option C) is the correct answer.