A 1 Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:. A 1 A apply mathematics to problems arising in everyday life, society, and the workplace. A 1 D communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.
A 3 Linear functions, equations, and inequalities. The student applies the mathematical process standards when using graphs of linear functions, key features, and related transformations to represent in multiple ways and solve, with and without technology, equations, inequalities, and systems of equations.
A 3 C graph linear functions on the coordinate plane and identify key features, including x -intercept, y -intercept, zeros, and slope, in mathematical and real-world problems.
Given algebraic, tabular, and graphical representations of linear functions, the student will determine the x - and y -intercepts of the function and interpret the meaning of intercepts within the context of the situation. How can you determine the x -intercept and y -intercept by looking at an equation? Linear functions can appear in a variety of representations. Through this exercise, you will investigate different ways to determine and interpret the intercepts of a linear function.
An intercept of any function is a point where the graph of the function crosses, or intercepts, the x -axis or y -axis. Because there are two axes on a coordinate plane, there can be a x -intercept , which is the point where the graph crosses the x -axis horizontal axis , or a y -intercept , which is the point where the graph crosses the y -axis vertical axis or both.
When the linear function is used to represent a real-world situation, the intercepts have significant meaning in the context of the problem. How can you distinguish between the x -intercept and the y -intercept from a graph? Interpret both the x - and y -intercepts in the relationships shown in the graphs below.
A hiker is hiking down a canyon toward the canyon floor. On the graph below you can see her height above the canyon floor as a function of time. If the sum of both the intercepts of the line is equal to 6, find the value of a. We can apply regular methods to solve a quadratic equation and calculate the value of x-intercepts. It means that the graph is crossing the x-axis at two different points.
The x-intercept means a coordinate plotted on the x-axis for any given curve. In other words, it is the value of the x coordinate of the point where the graph cuts the x-axis, or we can say that the x-intercept is the value of the x coordinate of a point where the value of y coordinate is equal to zero.
The value of x so obtained is the x-intercept of the curve. The x-intercept of any curve can be obtained using a similar technique. We just have to put the value of y as 0 in the equation of the curve.
We can calculate the x-intercept by putting y as 0. The slope and y - intercept values indicate characteristics of the relationship between the two variables x and y. The slope indicates the rate of change in y per unit change in x. The y - intercept indicates the y -value when the x-value is 0. So that means that our y-value, our water value is down at zero. And that happens on the graph right over there. And this point where the graph intersects the x -axis, that's known as the x - intercept.
What does Y intercept represent in a graph? In analytic geometry, using the common convention that the horizontal axis represents a variable x and the vertical axis represents a variable y, a y-intercept or vertical intercept is a point where the graph of a function or relation intersects the y-axis of the coordinate system. What does the slope represent?
Slope or Gradient We call m the slope or gradient of the line. It represents the change in y-value per unit change in x-value. Here are some points on the line. Click to see full answer Consequently, what does it mean to interpret the x and y intercepts?
The x - intercepts are where the graph crosses the x -axis, and the y - intercepts are where the graph crosses the y -axis. Then, algebraically, an x - intercept is a point on the graph where y is zero, and. Also, what does an intercept represent? Start with a regression equation with one predictor, X. If X sometimes equals 0, the intercept is simply the expected mean value of Y at that value. If X never equals 0, then the intercept has no intrinsic meaning. To find the x intercept using the equation of the line , plug in 0 for the y variable and solve for x.
You can also use the graph of the line to find the x intercept. Just look on the graph for the point where the line crosses the x -axis, which is the horizontal axis. That point is the x intercept. The y intercept is used in describing a line in 2D. C is the y - intercept and m is the slope of the line. This can also describe a physical relationship. The y intercept is the value of one variable when the other is zero. The x - intercept is where a line crosses the x -axis, and the y- intercept is the point where the line crosses the y-axis.
0コメント