Ozzie filled up the gas tank of his truck and headed out on a road trip. The x — axis on the graph below shows the number of miles Ozzie drove since filling up. How do you find the x — intercept of the graph of? Do you prefer to use the method of plotting points or the method using the intercepts to graph the equation? What steps will you take to improve? Skip to content Graphs. Learning Objectives By the end of this section, you will be able to: Identify the — and — intercepts on a graph Find the — and — intercepts from an equation of a line Graph a line using the intercepts.
Before you get started, take this readiness quiz. Solve: If you missed this problem, review Figure. Identify the x — and y — Intercepts on a Graph Every linear equation can be represented by a unique line that shows all the solutions of the equation. Intercepts of a Line.
Examples of graphs crossing the x-negative axis. Find the x — and y — Intercepts from an Equation of a Line Recognizing that the x — intercept occurs when y is zero and that the y — intercept occurs when x is zero, gives us a method to find the intercepts of a line from its equation.
Find the x — and y — Intercepts from the Equation of a Line. Graph a Line Using the Intercepts To graph a linear equation by plotting points, you need to find three points whose coordinates are solutions to the equation. How to Graph a Line Using Intercepts. Graph a linear equation using the intercepts.
Key Concepts Find the x — and y — Intercepts from the Equation of a Line Use the equation of the line to find the x — intercept of the line, let and solve for x. Use the equation of the line to find the y — intercept of the line, let and solve for y.
Graph a Linear Equation using the Intercepts Find the x — and y — intercepts of the line. Let and solve for x. Let and solve for y. Find a third solution to the equation.
Plot the three points and then check that they line up. Draw the line. If it only has one variable, it is a vertical or horizontal line. If y is isolated on one side of the equation, graph by plotting points. Choose any three values for x and then solve for the corresponding y — values. If the equation is of the form , find the intercepts. Find the x — and y — intercepts and then a third point. Practice Makes Perfect Identify the x — and y — Intercepts on a Graph In the following exercises, find the x — and y — intercepts on each graph.
Use a straightedge to create a nice straight line. Add an arrow on either end to indicate that the line continues indefinitely in either direction.
Solution: Begin by determining the x - and y -intercepts. Next, graph the two points and draw a line through them with a straightedge.
Here the x - and y -intercepts are actually the same point, the origin. We will need at least one more point so that we can graph the line. Choose any value for x and determine the corresponding value for y. To summarize, any linear equation can be graphed by finding two points and connecting them with a line drawn with a straightedge. This method for finding intercepts will be used throughout our study of algebra. The x - and y -intercepts are important points on any graph.
This chapter will focus on the graphs of linear equations. However, at this point, we can use these ideas to determine intercepts of nonlinear graphs. Remember that intercepts are ordered pairs that indicate where the graph intersects the axes. Example 6: Find the x - and y -intercepts given the following graph:. Solution: We see that the graph intersects the x -axis in two places.
Furthermore, the graph intersects the y -axis in one place. In our study of algebra, we will see that some graphs have many intercepts. Also, we will see that some graphs do not have any. Example 7: Given the following graph, find the x - and y -intercepts:. Solution: This is a graph of a circle; we can see that it does not intersect either axis. Once these have been found, we can plot them, draw a straight line connecting them, and extend the line at either end.
It is important to point out that, no matter what technique we use to graph an equation, the graph of the equation is always the same -- all techniques will yield the exact same graph. SparkTeach Teacher's Handbook. Summary Graphing Equations Using Intercepts.
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