Skip to main content. Module Graphs. Search for:. Identifying the Intercepts on the Graph of a Line Learning Outcomes Identify the x and y-intercepts of a line given in equation form Identify the x and y-intercepts of a line given in graph form.
If a line is parallel to one of the axes, then it will never intersect that axis. Since we see that our equation and that of the x-axis have the same slope , they will never intersect. Is it possible for a line to have no x-intercept? David Drayer. May 24, Explanation: A line with a slope of zero O will be parallel to the x axis. 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. In that case, you will end up with a vertical line. Even though you do not see an x in the equation, you can still graph it on a two dimensional graph.
If all the points are solutions then any ordered pair that has an y value of c would be a solution. As long as y never changes value, it is always c, then you have a solution. In that case, you will end up with a horizontal line.
With that in mind, what kind of line are we going to end up with? Note how the directions did not specify that we had to use intercepts to do our graph. Any time you take a math test or do homework, make sure that you follow directions carefully. If it specifies a certain way to do a problem, then you need to follow that plan like in the above examples 1 and 2.
Do we have a x-intercept? The answer is no. Since y has to be 4, then it can never equal 0, which is the criteria of an x -intercept. Also, think about it, if we have a horizontal line that crosses the y- axis at 4, it will never ever cross the x- axis. So, some points that we can use are 0, 4 , 1, 4 and 2, 4. These are all ordered pairs that fit the criteria of y having to be 4.
Of course, we could have used other solutions, there are an infinite number of them. It does not matter what y is, as long as x is Note that the x -intercept is at -3, 0. Do we have a y -intercept? Since x can never equal 0, then there will be no y-intercept for this equation.
Some points that would be solutions are -3, 0 , -3, 1 , and -3, 2. Again, I could have picked an infinite number of solutions. Practice: Intercepts from a table. Intercepts of lines review x-intercepts and y-intercepts. Next lesson. Current timeTotal duration Google Classroom Facebook Twitter.
Video transcript The graph of the line 2y plus 3x equals 7 is given right over here. Determine its x-intercept.
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