What is slope of a line

Every line has a consistent slope. In other words, the slope of a line never changes. This fundamental idea means that you can choose any 2 points on a line. Think about the idea of a straight line. If the slope of a line changed, then it would be a zigzag line and not a straight line, as you can see in the picture above.

What is the slope of a line that goes through the points 10,3 and 7, 9? A line passes through 4, -2 and 4, 3. What is its slope? A line passes through 2, 10 and 8, 7. A line passes through 7, 3 and 8, 5. A line passes through 12, 11 and 9, 5. What is the slope of a line that goes through 4, 2 and 4, 5? She was having a bit of trouble applying the slope formula, tried to calculate slope 3 times, and she came up with 3 different answers. Can you determine the correct answer?

In attempt 1, she did not consistently use the points. What she did, in attempt one, was :. The problem with attempt 3 was reversing the rise and run. She put the x values in the numerator top and the y values in the denominator which, of course, is the opposite! You can practice solving this sort of problem as much as you would like with the slope problem generator below.

It will randomly generate numbers and ask for the slope of the line through those two points. You can chose how large the numbers will be by adjusting the difficulty level.

Positive slope Here, y increases as x increases, so the line slopes upwards to the right. The slope will be a positive number. Negative slope Here, y decreases as x increases, so the line slopes downwards to the right.

The slope will be a negative number. The line on the right has a slope of about Zero slope Here, y does not change as x increases, so the line in exactly horizontal. The slope of any horizontal line is always zero. The line on the right goes neither up nor down as x increases, so its slope is zero. Undefined slope When the line is exactly vertical, it does not have a defined slope. The two x coordinates are the same, so the difference is zero.

The slope calculation is then something like When you divide anything by zero the result has no meaning. The line above is exactly vertical, so it has no defined slope. We say "the slope of the line AB is undefined". You do not need the graph to find the slope. You can just use the coordinates, keeping careful track of which is Point 1 and which is Point 2.

Notice that regardless of which ordered pair is named Point 1 and which is named Point 2, the slope is still 3. What is the slope of the line that contains the points [latex] 3, No matter which two points you choose on the line, they will always have the same y -coordinate. But there are two other kinds of lines, horizontal and vertical. What is the slope of a flat line or level ground? Of a wall or a vertical line? You can also use the slope formula with two points on this horizontal line to calculate the slope of this horizontal line.

So, when you apply the slope formula, the numerator will always be 0. Zero divided by any non-zero number is 0, so the slope of any horizontal line is always 0. How about vertical lines? In their case, no matter which two points you choose, they will always have the same x -coordinate. So, what happens when you use the slope formula with two points on this vertical line to calculate the slope? But division by zero has no meaning for the set of real numbers. Because of this fact, it is said that the slope of this vertical line is undefined.

This is true for all vertical lines—they all have a slope that is undefined. When you graph two or more linear equations in a coordinate plane, they generally cross at a point. However, when two lines in a coordinate plane never cross, they are called parallel lines. You will also look at the case where two lines in a coordinate plane cross at a right angle.

These are called perpendicular lines. The slopes of the graphs in each of these cases have a special relationship to each other. Parallel lines are two or more lines in a plane that never intersect. Examples of parallel lines are all around us, such as the opposite sides of a rectangular picture frame and the shelves of a bookcase. Perpendicular lines are two or more lines that intersect at a degree angle, like the two lines drawn on this graph.

These degree angles are also known as right angles. Perpendicular lines are also everywhere, not just on graph paper but also in the world around us, from the crossing pattern of roads at an intersection to the colored lines of a plaid shirt. The slope of both lines is 6. They are not the same line. The slopes of the lines are the same and they have different y -intercepts, so they are not the same line and they are parallel.

Two non-vertical lines are perpendicular if the slope of one is the negative reciprocal of the slope of the other. You can also check the two slopes to see if the lines are perpendicular by multiplying the two slopes together. In the case where one of the lines is vertical, the slope of that line is undefined and it is not possible to calculate the product with an undefined number.

Massive amounts of data is being collected every day by a wide range of institutions and groups. This data is used for many purposes including business decisions about location and marketing, government decisions about allocation of resources and infrastructure, and personal decisions about where to live or where to buy food. In the following example, you will see how a dataset can be used to define the slope of a linear equation.

Linear equations describing the change in median home values between and in Mississippi and Hawaii are as follows:. The slopes of each equation can be calculated with the formula you learned in the section on slope.

A linear equation describing the change in the number of high school students who smoke, in a group of , between and is given as:. Okay, now we have verified that data can provide us with the slope of a linear equation.

So what? We can use this information to describe how something changes using words. The following table pairs the type of slope with the common language used to describe it both verbally and visually.