The Algebra of Lines:In this lesson, we learn how to graph our line using the y-intercept and the slope. First, we know that the y-intercept (b) is on the y-axis, so we graph that point. Next, we use the slope to find a second point in relation to that intercept. The following video will show you how this is done with two examples. Show Video Source (05:37 mins) | Transcript Steps for graphing an equation using the slope and y-intercept:
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How Do You Find the Slope of a Line from a Graph?Trying to find the slope of a graphed line? First, identify two points on the line. Then, you could use these points to figure out the slope. In this tutorial, you'll see how to use two points on the line to find the change in 'y' and the change in 'x'. Then, you'll see how to take these values and calculate the slope. Check it out! Graphing a Line using the x and y-InterceptsAnother method to graph a line in the XY-plane is to use the intercepts. What are intercepts? These are points of the line that are found on the \color{red}\large{x} and \color{red}\large{y} axes. There are two kinds of intercepts.
Here is a quick diagram that gives you the idea.  Since the x-intercept is a point where the line crosses the x-axis, it is a point with a y-value of zero. In the same manner, since the y-intercept is a point where the line crosses the y-axis, it must be a point with an x-value of zero. Using the informal definitions of x and y-intercepts above, it makes a lot of sense why the procedures below on how to find them work! Rules on How to Find the Intercepts
Let y = 0 in the equation, then solve for x.
Let x = 0 in the equation, then solve for y. Examples of How to Graph a Line using the x and y-interceptsExample 1: Graph the equation of the line 2x-4y=8 using its intercepts. I hope you recognize that this is an equation of a line in Standard Form where both the x and y variables are found on one side of the equation opposite the constant term. It is a common practice in an algebra class to ask students to graph the line using the intercept method when the line is in Standard Form. Here we go!
Let y=0 in the equation, then solve for x. The x-intercept is (4, 0).
Let x=0 in the equation, then solve for y. The y-intercept is (0, –2). Now we can plot the two points on the xy axis and connect them using a straight edge ruler to show the graph of the line. Example 2: Graph the equation of the line using its intercepts. This equation of the line is in the Slope-Intercept Form. We can actually graph this using another technique which uses the slope and the y-intercept taken directly from the equation. You can see a separate lesson on how to graph a line using slope and y-intercept. Since this lesson is about intercepts, let’s work this out using this method.
Let y=0 in the equation, then solve for x. The x-intercept is (–2, 0).
Let x=0 in the equation, then solve for y. The y-intercept is (0, 3). Plot the intercepts in the axes and draw a straight line passing through them using a ruler. You might also be interested in: Three Ways to Graph a Line How do you find the intercepts for the graph of the equation?To find the x-intercept we set y = 0 and solve the equation for x. This is because when y=0 the line crosses the x-axis. When an equation is not in y = mx + b form, we can solve for the intercepts by plugging in 0 as needed and solving for the remaining variable. To find y-intercept: set x = 0 and solve for y.
How do you find intercepts from points?x-intercept is (x, 0). Since the x-coordinate is 0 for y-intercept, substitute the 0 for x in the equation. Similarly, find the x-intercept by replacing y with 0. You finally get the x-intercept as (14/3,0),and the y-intercept as (0,-7/2).
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Find the intercepts and graph the equation by plotting points
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