The reason why will be obvious in the next section. The other lines now have negative slopes and slant downwards from left to right. Each slope is the negative for the same-color line in Graph A. Jump to: navigation , search. Lines with positive slopes. Category : Algebra. 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:.
And is based on the data from this table, provided by the Centers for Disease Control. 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. Skip to main content. Module 2: Graphing. Search for:. Example Use the graph to find the slope of the line. The rise is 2 units. It is positive as you moved up.
Count the number of units. The run is 4 units. It is positive as you moved to the right. Example Use the graph to find the slope of the two lines. Show Solution Notice that both of these lines have positive slopes, so you expect your answers to be positive.
This line has a rise of 4 units up, so it is positive. The slope is 3. The example below shows the solution when you reverse the order of the points, calling 5, 5 Point 1 and 4, 2 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 3, The slope is The correct answer is. Put the coordinates into the slope formula consistently:. You have interchanged the rise and the run. Advanced Question. What is the slope of a line that includes the points and? It looks like you inverted the rise and the run. Use the formula to find the slope. It looks like you subtracted either the y or x coordinates in the wrong order. Make sure you subtract , then , and then calculate the slope.
Using the formula for slope, , you found that. Finding the Slopes of Horizontal and Vertical Lines. 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?
No matter which two points you choose on the line, they will always have the same y -coordinate. You can also use the slope formula with two points on this horizontal line to calculate the slope of this horizontal line. The slope of this horizontal line is 0. 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? Using 2, 1 as Point 1 and 2, 3 as Point 2, you get:. 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. The slope is 0, so the line is horizontal. Which of the following points will lie on the line created by the points and? Notice that both points on the line have the same x -coordinate but different y -coordinates. That makes it a vertical line, so any other points on the line will have an x -coordinate of The points and form a vertical line, so any other point on that line will have to have an x -coordinate of Try drawing a quick sketch of the points and.
They form a vertical line, so any other points on the line will have an x -coordinate of 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. The images below summarize the slopes of different types of lines. Example Problem Use the graph to find the slope of the line.
Answer The slope is. Example Problem Use the graph to find the slope of the two lines. Answer The slope of the blue line is 4 and the slope of the red line is. Example Problem Find the slope of the line graphed below. Answer The slope of the line is. Advanced Example Problem Find the slope of the line graphed below. Answer The slope of the line is 0. B 2 Incorrect. D Incorrect.
0コメント