Which of the following equations is parallel to x = 7 and passes through the point (6,-9)?
Responses
x = 6
x = 6
x = -9
x = -9
y = 6
y = 6
y = -9
y = -9
y = -9
To determine which equation is parallel to x = 7 and passes through the point (6, -9), we need to first understand what the equation x = 7 represents. This equation states that the x-coordinate of every point on the line is equal to 7. Therefore, any line that is parallel to x = 7 will have the same x-coordinate for all its points.
Looking at the given options, we can eliminate the equations y = 6 and y = -9 as they represent horizontal lines. The equation y = 6 is a horizontal line passing through y = 6, and the equation y = -9 is a horizontal line passing through y = -9.
Now let's evaluate the remaining equations: x = 6, x = -9, y = 6, and y = -9.
The equation x = 6 represents a vertical line passing through x = 6. This line is not parallel to x = 7.
The equation x = -9 also represents a vertical line passing through x = -9. This line is not parallel to x = 7.
The equation y = 6 represents a horizontal line passing through y = 6. This line is not parallel to x = 7.
Finally, the equation y = -9 represents a horizontal line passing through y = -9. This line is also not parallel to x = 7.
Therefore, none of the given equations is parallel to x = 7 and passes through the point (6, -9).
To determine which equation is parallel to x = 7 and passes through the point (6, -9), we need to observe the characteristics of the given equation.
The equation x = 7 represents a vertical line that crosses the x-axis at x = 7. A line parallel to this line would have the same slope, which means it would also be a vertical line.
A vertical line doesn't have a y-intercept since it is parallel to the y-axis and has the equation x = k, where k is a constant.
Now, let's analyze the given options:
1. x = 6: This equation represents a vertical line passing through the point (6, 0), so it is not parallel to x = 7.
2. x = -9: This equation represents a vertical line passing through the point (-9, 0), so it is not parallel to x = 7.
3. y = 6: This equation represents a horizontal line passing through the point (0, 6) and is not parallel to x = 7.
4. y = -9: This equation represents a horizontal line passing through the point (0, -9) and is not parallel to x = 7.
Based on our observations, none of the given options is parallel to x = 7 and passes through the point (6, -9).