![]() If your final solution contained one of the less than symbols, draw the arrow to the left. Draw a dark arrow from your dot that points in the direction of the inequality symbol. If, on the other hand, the symbol is either, draw an "open dot," or a circle, at the a value. If the inequality symbol allows for the possibility of equality (¤ or ¥), draw a solid dot at a. When you solve the inequality, you'll get something like this: x ¤ a or x > a, where a is a real number. It's sometimes more useful to center the number line at or near the value you found in the solution. The number line doesn't always have to be centered at 0. Before you can draw the graph of an inequality, you need to know its solution. For example, if you graph x > 7, you place an open dot at 7 because it's not a valid answer (7 is not greater than itself). Therefore, you don't need a coordinate plane to graph basic inequalities all you need is a number line, pictured in Figure 7.1 essentially, the number line is just the x-axis from the coordinate plane since there is no second variable, you don't need a second axis on the graph.Ī solid dot on a number line graph indicates that the given number should be included as a possible solution, whereas an open dot indicates that the given number cannot be a solution. However, basic inequalities (like those you just learned to solve in the previous section) are different than linear equations because they only contain one variable. You now know that basic inequalities have an infinite number of solutions, so you should also use graphs to help visualize their solutions. Because you couldn't write that infinite list of answers, it was useful to represent them with a drawing (graph) of the solutions. Since linear equations contained two variables, usually x and y, there were an infinite number of ordered pairs that made each equation true. ![]() The lines y = 2x + 1 and y = 2x + 3 are parallel, because both have a gradient of 2.In Graphing Linear Equations, when I was discussing linear equations, I explained why it was important to draw graphs. Two lines are parallel if they have the same gradent. If your graph is perfect, you should get an answer of 6 for the above question. The better your graph is, the closer your answer will be to the correct answer. Note: this method only gives an approximate answer. Gradient of tangent = (change in y)/(change in x) You then find the gradient of this tangent.įind the gradient of the curve y = x² at the point (3, 9). A tangent is a straight line which touches the curve at one point only. At the point where you need to know the gradient, draw a tangent to the curve. To find the gradient of a curve, you must draw an accurate sketch of the curve. Since the line crosses the y-axis when y = 3, the equation of this graph is y = ½x + 3. We can, of course, use this to find the equation of the line. In this graph, the gradient = (change in y-coordinate)/(change in x-coordinate) = (8-6)/(10-6) = 2/4 = 1/2 The gradient of the line = (change in y-coordinate)/(change in x-coordinate). For a straight-line graph, pick two points on the graph. It is often useful or necessary to find out what the gradient of a graph is. Finding the gradient of a straight-line graph
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