The \(y\)-intercept occurs when \(x\) is zero. The point where the line crosses the \(y\)-axis has the form \((0,b)\) and is called the \(y\) -intercept of the line. In each line, the \(x\) -coordinate of the point where the line crosses the \(y\)-axis is zero. The \(x\)-intercept occurs when \(y\) is zero. The point where the line crosses the \(x\)-axis has the form \((a,0)\) and is called the \(x\) -intercept of the line. Figureįor each line, the \(y\)-coordinate of the point where the line crosses the \(x\)-axis is zero. Now, let’s look at the points where these lines cross the \(y\)-axis. The points where a line crosses the \(x\)-axis and the \(y\)-axis are called the intercepts of the line.įirst, notice where each of these lines crosses the \(x\)-axis. In this figure, we have graphed a horizontal line passing through the \(y\)-axis at \(4.\) This time the y-value is a constant, so in this equation, \(y\) does not depend on \(x.\) Fill in \(4\) for all the \(y\)’s in Table and then choose any values for \(x.\) We’ll use 0, 2, and 4 for the \(x\)-coordinates. What if the equation has \(y\) but no \(x\)? Let’s graph the equation \(y=4\). Notice that we have graphed a vertical line. Plot the points from the table and connect them with a straight line. But to fit the points on our coordinate graph, we’ll use 1, 2, and 3 for the \(y\)-coordinates. Then choose any values for \(y.\) Since \(x\) does not depend on \(y,\) you can choose any numbers you like. So to make a table of values, write \(−3\) in for all the \(x\)-values. This equation has only one variable, \(x.\) The equation says that \(x\)is always equal to \(−3\), so its value does not depend on \(y.\) No matter what is the value of \(y,\) the value of \(x\) is always \(−3\). They may have just \(x\) and no \(y,\) or just \(y\) without an \(x.\) This changes how we make a table of values to get the points to plot. Some linear equations have only one variable. When an equation includes a fraction as the coefficient of \(x,\) we can still substitute any numbers for \(x.\) But the arithmetic is easier if we make “good” choices for the values of \(x.\) This way we will avoid fractional answers, which are hard to graph precisely. Look at the difference between these illustrations. This tells you something is wrong and you need to check your work. If you use three points, and one is incorrect, the points will not line up. If you only plot two points and one of them is incorrect, you can still draw a line but it will not represent the solutions to the equation. It is true that it only takes two points to determine a line, but it is a good habit to use three points. Extend the line to fill the grid and put arrows on both ends of the line. Draw the line through the three points. If they do not, carefully check your work.
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