Question

In the xy-plane, line k is paraliel to the line with equation y=7x+5. Which of the following could be an equation of line k ? a. y=-7x+5 b. y=-1/7x+4 c.y=5x+1/5 d.y=7x-1/5

Answer 1

To determine the equation of a line that is parallel to y = 7x + 5, we need to find a line with the same slope. Option D, y = 7x - 1/5, has the same slope and could be the equation of a line parallel to y = 7x + 5.

Step-by-step explanation:

To determine the equation of a line that is parallel to the line y = 7x + 5, we need to find a line with the same slope. The slope of the given line is 7. So, any line with a slope of 7 would be parallel to it.

A. y = -7x + 5 has a slope of -7, so it is not parallel to the given line.

B. y = -1/7x + 4 has a slope of -1/7, which is not the same as the slope of the given line, so it is not parallel.

C. y = 5x + 1/5 has a slope of 5, which is not the same as the slope of the given line, so it is not parallel.

D. y = 7x - 1/5 has a slope of 7, which is the same as the slope of the given line. Therefore, option D could be the equation of a line that is parallel to the line y = 7x + 5.

Answer 2

To answer this question, we need to understand the properties of parallel lines. Two lines in a plane are parallel if and only if they have the same slope.

The given equation of line is y = 7x + 5. The coefficient of x in this equation is the slope of the line. Therefore, the slope of the given line is 7.

So, the line k which is parallel to the given line must also have a slope of 7. Now, let's check the slope in each of the given options:

Option a. The equation is y = -7x + 5. Here the coefficient of x is -7, which is not equal to 7. So, option a cannot be an equation of line k.

Option b. The equation is y = -1/7x + 4. Here the coefficient of x is -1/7, which is also not equal to 7. So, option b cannot be an equation of line k.

Option c. The equation is y = 5x + 1/5. Here the slope or the coefficient of x is 5, which does not equal to 7. So, option c cannot be an equation of line k.

Option d. The equation is y = 7x - 1/5. Here, the coefficient of x is 7, which equals the slope of the given line. Therefore, option d could be an equation of line k.

In conclusion, the equation of k that is parallel to the line y=7x+5 could be y=7x-1/5. Therefore, the correct answer is d.