The graph of the equation contains the points 10, 0 and 0, You could plot these two points and connect them to determine the graph of the line.
Compare the Slopes of Lines. Consider two different non-vertical lines 1 and 2. Line 1 has a slope, m 1 , and line 2 has a slope, m 2. The lines are perpendicular if their slopes are negative reciprocals of each other. You can also use a table of values to determine and interpret the intercepts of a function.
The graph below represents the relationship between the floor number and the amount of time that Senedra has been in an elevator. Senedra is in an office building in Europe, where the ground floor is labeled "Floor 0" and the next floor up is labeled "Floor 1. Copy and paste the table below into your notes.
Use the elevator graph above to complete the table. Click on the plus sign to check your answers. Interpret both the x - and y -intercepts in the relationships shown in the tables below. The table below shows the distance remaining in a bus trip from Houston to Dallas as a function of time. How far is it in miles from Houston to Dallas? How many hours will the trip take? A farmer has a field of a certain size in which he or she can decide to plant corn or wheat.
The number of bushels of corn or wheat that the farmer can harvest from the field is shown in the table below. How many bushels can be harvested if he or she only plants corn? How many bushels can be harvested if he or she only plants wheat? In addition to determining and interpreting intercepts from graphs and tables, you can also determine and interpret intercepts directly from an equation.
To determine an intercept from an equation, simply substitute 0 and solve for the other variable. In the problems below, drag the mathematical steps of solving the equation into the correct descending order in each row. Use the completed solutions to look for patterns in how you can determine the x -intercept and y -intercept for a linear equation that is given in slope-intercept form.
Use the completed solutions to look for patterns in how you can determine the x -intercept and y -intercept for a linear equation that is given in standard form.
So now you've investigated several different ways to determine the x -intercept and y -intercept of a linear function. You used graphs, tables, and equations to determine the intercepts of linear functions.
You also investigated how to interpret the intercepts within the context of a situation. In each representation, the x -intercept is the point where the graph of the line crosses the x -axis, or the ordered pair x , 0.
The y -intercept is the point where the graph of the line crosses the y -axis, or the ordered pair 0, y. Skip to main content. Learning Objectives. Introduction In Tutorial Graphing Linear Equations , we went over graphing linear equations by plotting points. In this tutorial the concept of using intercepts to help graph will be introduced, as well as vertical and horizontal lines.
Actually, the process of graphing by plotting points and graphing by using intercepts are essentially the same. Intercepts are just special types of solutions, but solutions none the less. So once we find them, we plot them just the same as any other ordered pair that is a solution. Once we plot them, we draw our graph in the same fashion as when we had non-intercept points. So, basically, when you graph, you plot solutions whether they are intercept points or not and connect the dots to get your graph.
Just keep in mind that intercepts work with the number 0, which is a nice easy number to work with when plugging in and solving.
It is one of those types of problems that I warn students to not make harder than it is. The word 'intercept' looks like the word 'intersect'. Think of it as where the graph intersects the x-axis. With that in mind, what value is y always going to be on the x -intercept? We will use that bit of information to help us find the x -intercept when given an equation. We will use this tidbit to help us find the y -intercept when given an equation.
Below is an illustration of a graph of a linear function which highlights the x and y intercepts:. In the above illustration, the x -intercept is the point 2, 0 and the y -intercept is the point 0, 3. Keep in mind that the x- and y- intercepts are two separate points.
There is only one point that can be both an x- and y- intercept at the same time, do you know what point that is? If you said the origin 0, 0 , give yourself a pat on the back. You find the y- intercept by plugging in 0 for x and solving for y. This is just like we showed you in Tutorial Graphing Linear Equations. Next, we will find the y- intercept. What value are we going to plug in for x? Note that we could have plugged in any value for x: 5, 10, , Next, we will find the y - intercept.
Hey, look at that, we ended up with the exact same point for both our x - and y- intercepts. As mentioned above, there is only one point that can be both an x - and y - intercept at the same time, the origin 0, 0.
We can plug in any x value we want as long as we get the right corresponding y value and the function exists there. Even though you do not see a y in the equation, you can still graph it on a two dimensional graph.
Remember that the graph is the set of all solutions for a given equation. If all the points are solutions then any ordered pair that has an x value of c would be a solution. As long as x never changes value, it is always c , then you have a solution.
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