Question

Find the equation for the horizontal line that goes through point M(a, b).

What is the equation of the horizontal line passing through point M(a, b)?
a) y = a
b) y = b
c) x = a
d) x = b

Answer 1

The equation of a horizontal line passing through point M(a, b) is given by the equation y = b, representing a line where the y-value remains constant and parallel to the x-axis.

Step-by-step explanation:

The equation of a horizontal line that passes through a point M(a, b) is very straightforward. Since horizontal lines have a slope (m) of 0, there is no rise over run. The value of 'y' remains constant regardless of the value of 'x'. Thus, for every point on this line, the y-coordinate will be 'b', the same as the y-coordinate of point M.

In clear terms, the correct equation is: y = b. This indicates a line where every point's y-value is equal to 'b', and this line will be parallel to the x-axis. So, the answer to the student's question is b) y = b.

Answer 2

The equation of the horizontal line passing through point M(a, b) is y = b.

Step-by-step explanation:

The equation of a horizontal line is of the form y = b, where b represents the y-coordinate of any point on the line.

Since the line passes through point M(a, b), the equation of the horizontal line is y = b.