8x + 2y = 7
2y = -8x + 7
y = -4x + 7/2; this line has slope equal -4
Parallel lines, slope is the same so slope of parallel line is also -4
A. y − 1 = 4(x + 8); slope m = 4....FALSE
B. y = −4x + 15; slope m = - 4....TRUE
C. 16x + 4y = 9; 4y = -16x + 9 so y = -4x + 9/4; slope m = - 4....TRUE
D. y = −4x; slope m = - 4....TRUE
Answer
B. y = −4x + 15
C. 16x + 4y = 9
D. y = −4x
The general form of the straight line equation is y = m·x + c
The lines that are parallel to 8·x + 2·y = 7, are;
B. y = -4·x + 15
C. 16·x + 4·y = 9
D. y = -4·x
The reason the above values are correct are as follows;
The given line is 8·x + 2·y = 7
Required:
To find the line parallel to the given line, 8·x + 2·y = 7
Solution:
Two lines are parallel if they have the same slope but different y-intercept
The slope of the given line is given by the value of m when the line is represented in the form y = m·x + c
8·x + 2·y = 7
2·y = 7 - 8·x
Dividing both sides by two gives;
[tex]\dfrac{2 \cdot y}{2} = \dfrac{7}{2} - \dfrac{8\cdot x}{2}\\[/tex]
Therefore;
[tex]y= \dfrac{7}{2} - {4\cdot x}[/tex]
The slope of the line is therefore, m = -4
The y-intercept of the line, c = [tex]\dfrac{7}{2}[/tex]
We check the slope of each of the given lines as follows;
Option A; y - 1 = 4·(x + 8)
The slope of the line in option A is 4·x, therefore, oy - 1 = 4·(x + 8), is not parallel to 8·x + 2·y = 7
Option B. y = -4·x + 15
The slope of the line in option B is also m = -4·x, and the y-intercept is c = 15, is different from the y-intercept of the given function
Therefore, the line y = -4·x + 15, is parallel to 8·x + 2·y = 7
Option C. 16·x + 4·y = 9
The line given by the equation in option C. can be rearranged as follows;
4·y = 9 - 16·x
Therefore, we have;
[tex]\dfrac{4 \cdot y}{4} = \dfrac{9}{4} - \dfrac{16 \cdot x}{4}[/tex]
[tex]y = \dfrac{9}{4} - 4 \cdot x}[/tex]
Therefore, the slope of the equation in option C, is also m = -4
Therefore, the equation in option C. is also parallel to the given equation
Option D. y = -4·x
The slope of the function in option D, given in the form of y = m·x + c is m = -4, and c = 0
Therefore, the equation in option D is also parallel to the given function
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