Use a ruler to join them with a straight line. Go back and calculate again. Method 2. Rearrange the function to make y the subject. Move everything but y to the left, as follows. In the rewritten example above, you might choose to use -1, 0, and 1 as your x values.
Solve as follows. Can a graph of a linear function have an inconsistent not constant rate of change? It all depends on the function equation you are given. Try researching other linear functions for similarities. Yes No. Not Helpful 2 Helpful 3. Include your email address to get a message when this question is answered. By using this service, some information may be shared with YouTube. Linear functions have many practical applications, especially in economics. Helpful 1 Not Helpful 1.
Functions have one independent x and one dependent y variable. The slope a of a line passing through points x1, y1 and x2, y2 is calculated as follows.
Helpful 0 Not Helpful 0. Submit a Tip All tip submissions are carefully reviewed before being published. Related wikiHows How to. How to. Co-authors: Updated: December 5, Categories: Algebra.
Thanks to all authors for creating a page that has been read 27, times. Did this article help you? Cookies make wikiHow better. By continuing to use our site, you agree to our cookie policy. About This Article. By signing up you are agreeing to receive emails according to our privacy policy. Follow Us. The steepness, or incline, of a line is measured by the absolute value of the slope. A slope with a greater absolute value indicates a steeper line.
In many cases, we can find slope by simply counting out the rise and the run. We start by locating two points on the line. If possible, we try to choose points with coordinates that are integers to make our calculations easier. Find the slope of the line: Notice the line is increasing so make sure to look for a slope that is positive. Locate two points on the graph, choosing points whose coordinates are integers. Identify points on the line: Draw a triangle to help identify the rise and run.
Notice that the slope is positive since the line slants upward from left to right. Find the slope of the line: We can see the slope is decreasing, so be sure to look for a negative slope.
Locate two points on the graph. Look for points with coordinates that are integers. Notice that the slope is negative since the line slants downward from left to right. Two variables in direct variation have a linear relationship, while variables in inverse variation do not.
Simply put, two variables are in direct variation when the same thing that happens to one variable happens to the other. The two variables may be considered directly proportional. Thus we can say that the cost varies directly as the value of toothbrushes. Direct variation is represented by a linear equation, and can be modeled by graphing a line. Since we know that the relationship between two values is constant, we can give their relationship with:.
Doing so, the variables would abide by the relationship:. Any augmentation of one variable would lead to an equal augmentation of the other. Inverse variation is the opposite of direct variation. In the case of inverse variation, the increase of one variable leads to the decrease of another. In fact, two variables are said to be inversely proportional when an operation of change is performed on one variable and the opposite happens to the other.
As an example, the time taken for a journey is inversely proportional to the speed of travel. If your car travels at a greater speed, the journey to your destination will be shorter. Knowing that the relationship between the two variables is constant, we can show that their relationship is:. We can rearrange the above equation to place the variables on opposite sides:.
Notice that this is not a linear equation. It is impossible to put it in slope-intercept form. Thus, an inverse relationship cannot be represented by a line with constant slope. Inverse variation can be illustrated with a graph in the shape of a hyperbola, pictured below. Inversely Proportional Function: An inversely proportional relationship between two variables is represented graphically by a hyperbola. The graph of a linear function is a straight line.
Linear functions can have none, one, or infinitely many zeros. Finally, if the line is vertical or has a slope, then there will be only one zero. Zeros can be observed graphically. All lines, with a value for the slope, will have one zero. Since each line has a value for the slope, each line has exactly one zero. The zero from solving the linear function above graphically must match solving the same function algebraically. This is the same zero that was found using the graphing method.
The slope-intercept form of a line summarizes the information necessary to quickly construct its graph. One of the most common representations for a line is with the slope-intercept form. This assists in finding solutions to various problems, such as graphing, comparing two lines to determine if they are parallel or perpendicular and solving a system of equations. Simply substitute the values into the slope-intercept form to obtain:.
The value of the slope dictates where to place the next point. Using this information, graphing is easy. The point-slope equation is another way to represent a line; only the slope and a single point are needed. Use point-slope form to find the equation of a line passing through two points and verify that it is equivalent to the slope-intercept form of the equation. The point-slope equation is a way of describing the equation of a line.
Therefore, the two equations are equivalent and either one can express an equation of a line depending on what information is given in the problem or what type of equation is requested in the problem.
Plug this point and the calculated slope into the point-slope equation to get:.
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