You can start with 4, 3 or with 1, 2 and, either way, you end with the exact same number! Whenever zero is the denominator of the fraction in this case of the fraction representing the slope of a line, the fraction is undefined. Therefore, regardless of what the run is provided its' not also zero! Therefore, the slope must evaluate to zero. Below is a picture of a horizontal line -- you can see that it does not have any 'rise' to it.
Answer: Yes, and this is a fundamental point to remember about calculating slope. 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. The slope of a straight line is the ratio of the change in y to the change in x, also called the rise over run. Another way of saying this is that the slope is the rate of change of y with respect to x. Rise Over Run. So how do we find slope? The Slope Formula! Slope Formula Definition.
Example In the example to the right, we are asked to determine the slope of the line that passes through the ordered pairs -3,8 and 2, If you go down to get to your second point, the rise is negative. If you go right to get to your second point, the run is positive. If you go left to get to your second point, the run is negative.
You can also find the slope of a straight line without its graph if you know the coordinates of any two points on that line. Every point has a set of coordinates: an x -value and a y -value, written as an ordered pair x , y. The x value tells you where a point is horizontally. The y value tells you where the point is vertically. Consider two points on a line—Point 1 and Point 2. The rise is the vertical distance between the two points, which is the difference between their y -coordinates.
So you are going to move from Point 1 to Point 2. A triangle is drawn in above the line to help illustrate the rise and run. You can see from the graph that the rise going from Point 1 to Point 2 is 4, because you are moving 4 units in a positive direction up.
Using the slope formula,. 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.
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