The greater the slope the steeper the line. Slope means that a unit change in x, the independent variable will result in a change in y by the amount of b. Slope shows both steepness and direction. With positive slope the line moves upward when going from left to right.
With negative slope the line moves down when going from left to right. The slope of a linear function is the same no matter where on the line it is measured. 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.
The slope for the Mississippi home prices equation is positive , so each year the price of a home in Mississippi increases by dollars. We can apply the same thinking for Hawaii home prices. The slope for the Hawaii home prices equation tells us that each year, the price of a home increases by dollars.
Interpret the slope of the line describing the change in the number of high school smokers using words. Apply units to the formula for slope. The x values represent years, and the y values represent the number of smokers. Remember that this dataset is per high school students.
The slope of this linear equation is negative , so this tells us that there is a decrease in the number of high school age smokers each year.
On the next page, we will see how to interpret the y -intercept of a linear equation, and make a prediction based on a linear equation. Slope describes the steepness of a line. The slope of any line remains constant along the line. The slope can also tell you information about the direction of the line on the coordinate plane.
Slope can be calculated either by looking at the graph of a line or by using the coordinates of any two points on a line. If the line decreases along the y axis as it moves from left to right, it is said to have a negative slope. A line that moves horizontally or vertically without any movement along the other axis has zero slope with vertical lines sometimes being said to have infinite slope.
When sketching lines on a graph, lines with positive slope move "up" when traveling left to right while those with negative slope move "down. Slope is a measure of a line's rise the amount it changes along the y axis divided by its run the amount it changes along the x axis. The result can be positive or negative. Holding a BS in computer science and several years of experience building, repairing and maintaining computers and electronics, Jack Gerard has had a love of science and mathematics for years.
Since it is a ratio, it could also be represented as. Related Articles What is Zero Slope? How to Calculate Slope Ratio. What Is an Infinite Slope?
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