We can get down to business and answer our question of what are the slope and y -intercept. In our problem, that would have to be 2. In our problem, that would be Looking at the graph, you can see that this graph never crosses the y -axis, therefore there is no y -intercept either.
Another way to look at this is the x value has to be 0 when looking for the y -intercept and in this problem x is always 5. So, for all our efforts on this problem, we find that the slope is undefined and the y -intercept does not exist. Looking at the graph, you can see that this graph crosses the y -axis at 0, So the y-intercept is 0, The slope is 0 and the y -intercept is Note that two lines are parallel if there slopes are equal and they have different y -intercepts.
What do you think? The slope of the first equation is 7 and the slope of the second equation is 7. Since the two slopes are equal and their y -intercepts are different, the two lines would have to be parallel.
So what does that mean? Since the two slopes are negative reciprocals of each other, the two lines would be perpendicular to each other.
The slope of the first equation is and the slope of the second equation is Since the two slopes are not equal and are not negative reciprocals of each other, then the answer would be neither. At the link you will find the answer as well as any steps that went into finding that answer.
Practice Problem 1a - 1b: Find the slope of the straight line that passes through the given points. Practice Problems 2a - 2c: Find the slope and the y -intercept of the line. Practice Problems 3a - 3b: Determine if the lines are parallel, perpendicular, or neither. Practice Problem 4a: Determine the slope of the line. Need Extra Help on these Topics? After completing this tutorial, you should be able to: Find the slope given a graph, two points or an equation.
This tutorial takes us a little deeper into linear equations. Rise means how many units you move up or down from point to point. On the graph that would be a change in the y values. The subscripts just indicate that these are two different points. It doesn't matter which one you call point 1 and which one you call point 2 as long as you are consistent throughout that problem. 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. For any two distinct points on a line, x 1 , y 1 and x 2 , y 2 , the slope is,. Intuitively, we can think of the slope as measuring the steepness of a line. The slope of a line can be positive, negative, zero, or undefined. A horizontal line has slope zero since it does not rise vertically i.
As stated above, horizontal lines have slope equal to zero. This does not mean that horizontal lines have no slope. Functions represented by horizontal lines are often called constant functions. Vertical lines have undefined slope. Since any two points on a vertical line have the same x -coordinate, slope cannot be computed as a finite number according to the formula,.
This means for each unit increase in x , there is a corresponding m unit increase in y i. Lines with positive slope rise to the right on a graph as shown in the following picture,.
Lines with greater slopes rise more steeply. This means for each unit increase in x , there is a corresponding m unit decrease in y i. Lines with negative slope fall to the right on a graph as shown in the following picture,. The steepness of lines with negative slope can also be compared.
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