Which of the following equations is parallel to the x-axis and passes through the point (-2,10)?
Responses
x = -2
x = -2
y = -2
y = -2
x = 10
x = 10
y = 10
y = 10
y = 10
Which of the following lines is perpendicular 2x−y=10 to and passes through the point (-10,2)
To find a line that is perpendicular to 2x - y = 10, we need to find the line with a slope that is the negative reciprocal of the slope of the given line.
First, we need to rewrite the equation in slope-intercept form (y = mx + b):
2x - y = 10
-y = -2x + 10
y = 2x - 10
The slope of the given line is 2.
The negative reciprocal of 2 is -1/2.
Now, we can use the point-slope form of a line to find the equation of the perpendicular line:
y - y1 = m(x - x1)
Using the point (-10, 2) and the slope -1/2:
y - 2 = (-1/2)(x - (-10))
y - 2 = (-1/2)(x + 10)
y - 2 = (-1/2)x - 5
y = (-1/2)x - 3
So, the line that is perpendicular to 2x - y = 10 and passes through the point (-10,2) is y = (-1/2)x - 3.
The equation x = -2 is parallel to the x-axis and passes through the point (-2,10).
To determine which equation is parallel to the x-axis and passes through the point (-2,10), we need to understand the properties of the x-axis and the given point.
The x-axis is a horizontal line that extends infinitely in both directions. It runs parallel to the ground, meaning its equation will have a constant y-value.
The given point (-2,10) has an x-coordinate of -2 and a y-coordinate of 10. This means the x-value is fixed at -2, while the y-value can vary.
Now, let's analyze each equation:
1. x = -2: This equation represents a vertical line passing through the x-coordinate -2. It is not parallel to the x-axis because it has a varying y-value.
2. y = -2: This equation represents a horizontal line with a constant y-value of -2. It is not parallel to the x-axis because it runs parallel to the y-axis.
3. x = 10: This equation represents a vertical line passing through the x-coordinate 10. It is not parallel to the x-axis because it has a varying y-value.
4. y = 10: This equation represents a horizontal line with a constant y-value of 10. It is parallel to the x-axis since its y-value remains the same for every point on the line.
Therefore, the equation that is parallel to the x-axis and passes through the point (-2,10) is y = 10.