Which equation has a graph perpendicular to the graph of 7x = 14y – 8 ?
(1 point)
Responses
y = –2x – 7
y = –2 x – 7
y = –x + 4
y = – Image with alt text: one-half x + 4
y = x + 1
y = Image with alt text: one-half x + 1
y = 2x + 9
y = 2 x + 9
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The equation that has a graph perpendicular to the graph of 7x = 14y – 8 is y = –1/2 x + 4.
Which equation is the equation of a line that passes through (–10, 3) and is perpendicular to y = 5x – 7?
(1 point)
Responses
y = 5x + 53
y = 5 x + 53
y = –x – 7
y = – Image with alt text: one-fifth x – 7
y = –x + 1
y = – Image with alt text: one-fifth x + 1
y = x + 5
y = Image with alt text: one-fifth x + 5
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To find the equation of a line that is perpendicular to y = 5x - 7, we need to determine the negative reciprocal of the slope of the given line. The slope of y = 5x - 7 is 5, so the negative reciprocal of 5 is -1/5.
Using the point-slope form of a linear equation, we can plug in the coordinates (-10, 3) and the negative reciprocal slope (-1/5) to find the equation.
y - y1 = m(x - x1)
y - 3 = -1/5(x - (-10))
y - 3 = -1/5(x + 10)
y - 3 = -1/5x - 2
y = -1/5x + 1
Therefore, the equation of the line that passes through (-10, 3) and is perpendicular to y = 5x - 7 is y = -1/5x + 1.
Which of the following coordinates for P will make line MN perpendicular to line OP in the diagram below?
(1 point)
Responses
(–2, –5)
(–2, –5)
(–3, 6)
(–3, 6)
(3, 2)
(3, 2)
(3, 5)
(3, 5)
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To determine which coordinate will make line MN perpendicular to line OP, we need to consider the slopes of the lines. Two lines are perpendicular if and only if the product of their slopes is -1.
From the given diagram, we can assume that line OP has a known slope. However, without more specific information about the lines or the diagram, it is not possible to determine the slope of line OP or line MN. Therefore, we cannot determine which coordinate will make line MN perpendicular to line OP based on the information provided.
Segment XY represents the path of an airplane that passes through the coordinates (2, 1) and (4, 5). What is the slope of a line that represents the path of another airplane that is traveling parallel to the first airplane?
(1 point)
Responses
–2
–2
Image with alt text: negative one-half
Image with alt text: one-half
2
2
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To find the slope of a line that is parallel to the line represented by segment XY, we need to use the formula for calculating slope.
The slope formula is given by:
m = (y2 - y1) / (x2 - x1)
Using the coordinates (2, 1) and (4, 5), we can substitute these values into the slope formula:
m = (5 - 1) / (4 - 2)
m = 4 / 2
m = 2
Therefore, the slope of a line that represents the path of another airplane traveling parallel to the first airplane is 2.