Make sure that you are careful when one of your values is negative and you have to subtract it as we did in line 2. Example 2 : Find the slope of the straight line that passes through 1, 1 and 5, 1. It is ok to have a 0 in the numerator. Remember that 0 divided by any non-zero number is 0. Example 3 : Find the slope of the straight line that passes through 3, 4 and 3, 6. Since we did not have a change in the x values, the denominator of our slope became 0. This means that we have an undefined slope.
If you were to graph the line, it would be a vertical line, as shown above. If your linear equation is written in this form, m represents the slope and b represents the y -intercept. Example 4 : Find the slope and the y -intercept of the line. Lining up the form with the equation we got, can you see what the slope and y-intercept are? Example 5 : Find the slope and the y -intercept of the line.
This example is written in function notation, but is still linear. As shown above, you can still read off the slope and intercept from this way of writing it. Note how we do not have a y. This type of linear equation was shown in Tutorial Graphing Linear Equations.
If you said vertical, you are correct. Note that all the x values on this graph are 5. Well you know that having a 0 in the denominator is a big no, no. This means the slope is undefined. As shown above, whenever you have a vertical line your slope is undefined.
Note how we do not have an x. If you said horizontal, you are correct. Note how all of the y values on this graph are Division by zero is always undefined. Every point on this line has an x-coordinate of 4, so this will happen regardless of the points picked. Therefore, the slope formula will always result in division by zero and therefore the slope will be undefined.
We have seen how the slope of a line may be undefined. Warning: It is very common to confuse these two types of lines and their slopes, but they are very different. Just as "horizontal" is not at all the same as "vertical", so also "zero slope" is not at all the same as "no slope". Just as a "Z" with its two horizontal lines is not the same as an "N" with its two vertical lines , so also "Zero" slope for a horizontal line is not the same as "No" slope for a vertical line.
The number "zero" exists, so horizontal lines do indeed have a slope. But vertical lines don't have any slope; "slope" simply doesn't have any meaning for vertical lines. It is very common for tests to contain questions regarding horizontals and verticals. Don't mix them up! Page 1 Page 2 Page 3. All right reserved. Web Design by. Skip to main content. Purplemath Let's consider again the two equations we did first on the previous page, and compare the lines' equations with their slope values.
Content Continues Below. Parallel and perpendicular lines have very special geometric arrangements; most pairs of lines are neither parallel nor perpendicular. Parallel lines have the same slope. For example, the lines given by the equations,. These two lines have different y -intercepts and will therefore never intersect one another since they are changing at the same rate both lines fall 3 units for each unit increase in x.
The graphs of y 1 and y 2 are provided below,. Perpendicular lines have slopes that are negative reciprocals of one another. In other words, if a line has slope m 1 , a line that is perpendicular to it will have slope,.
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