Which of the following represent the equation of the line passing through (6, –10) and (6, –6)?
A) x = 6 B) y = 6
C) y = x + 6 D) y = 4x
My solution was
m = -6 +10 = 4/0
6 – 6
because 4 0ver 0 was the result of my solution I thought answer D (above) was my answer. But I'm having second thoughts. Please help
If you draw the two points and draw a line running through them, you see that the line is parallel to the y-axis and intersects the x-axis at x = 6. So, a point is on the line if and only if x = 6, regardless of the value of y.
The equation is thus x = 6.
The general equation for a line is:
a x + b y + c = 0
If b is not equal to zero then you can write this as a function of y in terms of x, like y = m x + s.
In this case, b = 0, so the equation is x = 6.
Answer: A) x = 6
In this case, the equation of the line passing through the points (6, -10) and (6, -6) cannot be expressed as a function of y in terms of x since the value of x is constant at x = 6. Therefore, the correct answer is A) x = 6.
To solve this problem, you correctly calculated the slope of the line using the formula (change in y)/(change in x). However, in this case, there is no change in x because both points have the same x-coordinate. This means that the line is vertical and parallel to the y-axis.
A vertical line can be written in the form x = k, where k is the x-coordinate of any point on the line. In this case, since both points have an x-coordinate of 6, the equation of the line is x = 6.
Therefore, the correct answer is A) x = 6.