Which of the following is always true about the graph of a horizontal line? *
1 point
A. The graph will have a positive y-intercept.
B. The graph will have a negative y-intercept.
C. The slope of the graph will be undefined.
D. The slope of the graph will be zero.
The correct answer is D. The slope of the graph will be zero. To understand why this is true, let's first review what a horizontal line looks like.
A horizontal line is a straight line that is parallel to the x-axis. This means that all the points on the line have the same y-coordinate but varying x-coordinates. For example, the equation of a horizontal line can be written as y = c, where c is a constant.
Now, to determine the slope of a line, we can use the formula m = (y₂ - y₁) / (x₂ - x₁), where (x₁, y₁) and (x₂, y₂) are any two points on the line. For a horizontal line, the y-coordinates of all points are the same, so the numerator (y₂ - y₁) will always be zero. Therefore, the slope will be zero divided by any non-zero value, which is always zero.
Hence, Option D is always true about the graph of a horizontal line.
slope is (change in y) / (change in x)
if the line is horizontal, the y values does not change, so ...