explain why you cannot use y=mx+b to find the equation of a veritcal line
m is undefined
IDK too
To understand why you cannot use the equation y = mx + b to find the equation of a vertical line, let's first examine the components of the equation.
In the equation y = mx + b:
- y represents the dependent variable or the vertical position.
- x represents the independent variable or the horizontal position.
- m represents the slope or the rate at which the line rises or falls.
- b represents the y-intercept or the point where the line intersects the y-axis.
Now, let's consider a vertical line. A vertical line is perfectly perpendicular to the x-axis and extends infinitely in both the positive and negative y-directions. Since a vertical line has no slope (or its slope is undefined), the equation of a vertical line cannot be represented by the slope-intercept form (y = mx + b) because the slope (m) is undefined.
When the slope (m) is undefined, it means that the vertical change, or the change in y, is infinite while the horizontal change, or the change in x, is zero. As a result, you cannot express the equation of a vertical line using the slope-intercept form as there is no finite value for the slope (m).
Instead, to represent a vertical line, you can use the equation of the form x = c, where c is the x-coordinate of any point on the line. This equation indicates that the value of x remains constant for every value of y along the line, which aligns with the vertical orientation of the line.