The difference in the y-coordinates is this: There are two points, each with its own coordinates. Where do these change in coordinates come from? Take a look at this example. What two numbers make up this ratio? As you can see from the definition, it’s the ratio of the change in y-coordinates over the change in x-coordinates. Recall that a ratio can look like a fraction and can be thought of as one number divided by another. To learn more about undefined slope, read the following background material. The vertical line test is used to determine if such graphs are functions. One of the ways to test if a graph is a function is if any two points share the same x-coordinate. The graph of such a line is a vertical line. In fact the equation of a vertical line is of the form x = c, for some constant c. With an undefined slope there is no equation in slope-intercept form. Since the equation for any line can be written in slope-intercept form, as shown below, what happens when the slope is undefined? So, what we've seen is that if two points have the same x-coordinate, then the line connecting them has an undefined slope. The fact that delta-x is zero means that the slope of the line is undefined. Plug in the values of the coordinates into the formula.īecause the x-coordinates are identical, the value for delta-x is zero.īut we know that a ratio cannot have zero in the denominator. To find the slope of the line connecting these two points, use the slope formula, as shown here. Notice that both points have the same x-coordinate, 1. It also means that each point has the same x-coordinate. Since the y-axis is a vertical axis, that means a line with an undefined slope is a vertical line. If you connect the points with a line, you'll see that this line is parallel with the y-axis. That means the two points are in this relative position. If delta-x equals zero, that means there is no horizontal separation between the two points. Let's place two points on a coordinate grid, like this.ĭelta-x is the horizontal separation between the two points. What does 'delta-x equals zero' correspond to? In order for the slope ratio to have a zero denominator, that means that delta-x would have to equal zero. That's because division by zero is undefined. When calculating slopes, the ratio is one number divided by another number.īy definition a ratio cannot have a denominator of zero.

Slope is defined as the ratio of the change in the y-coordinates over the change in the x-coordinates. Your browser does not support the video tag. Watch this video to learn about undefined slope. The slope of the line that crosses these two points has a slope of 1. That means that 7 minus 3 in the numerator and 6 - 2 in the denominator. Take those coordinates and plug them into the slope formula. For the purposes of the slope formula, let's call these coordinates x1 and y1, and let's call these coordinates x2 and y 2. To find the slope of the line that crosses these two points, use the slope formula.

This point has coordinates 2, 3 and this point has coordinates 6,7. Use those coordinates in the slope formula to calculate the slope. This one has coordinates x1 and y1 and this one has coordinates x2 and y2. When you know the coordinates of two points, use this version of the slope formula. In terms of the coordinates, it is the ratio in the difference in the y coordinates over the difference in the x coordinates. It is the ratio of the Rise over the Run, or the ratio of this vertical distance over this horizontal distance.

Use it when you want to find the slope of the line that connects two points.

Desmos activity graphing lines