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0:00 How to graph your answers: number lines

Some homework questions ask you to answer by drawing on a number line. Every example in this video uses the same graphing tool as your homework.

0:10 The graphing toolbar

Every graphing question has a graph and a row of tools under it. Pick a tool first, then click the graph. Number line questions use up to three tools: the Line segments and rays tool, the Closed dot tool, and the Open dot tool. Everything you draw stays on the line. Most graphs move each click to the nearest grid mark, so you don't need to click exactly on a mark. Clear All erases everything you drew on that graph. There is no undo. Whenever you need to redraw a graph, click Clear All. It clears only the graph it sits under: a question with two graphs has two Clear All buttons.

0:50 Example 1 · An inequality: one dot and a ray

Graph x is greater than or equal to negative two on the number line. Choose the Closed dot tool. The symbol greater than or equal to includes negative two, so its dot is filled in. Click negative two on the number line. Now choose the Line segments and rays tool. Click negative two to start the ray. Click the last number at the right end of the line, ten. An arrowhead appears, so the graph keeps going to the right.

1:20 Example 2 · An interval: two dots and a segment

Graph the interval from negative three to four, with a parenthesis at negative three and a square bracket at four, on the number line. Choose Open dot. The parenthesis leaves negative three out, so its dot is open. Click negative three on the number line. Choose Closed dot. The square bracket includes four. Click four on the number line. Choose Line segments and rays, then click negative three and four to join the dots.

1:51 Example 3 · Two pieces: rays going opposite ways

Graph x is less than negative one or x is greater than or equal to two on the number line. Choose Open dot and click negative one. The symbol less than leaves negative one out. Choose Closed dot and click two. The symbol greater than or equal to includes two. Choose Line segments and rays. Click negative one, then the first number at the left end, negative ten, to draw a ray going left. Click two, then the last number at the right end, ten, to draw the second ray.

2:27 Redraw with Clear All

The segment and its dots are separate pieces. If you move the end of a segment, move its dot too. There is no undo. If you need to redraw a graph, click Clear All and draw it again. Your drawing is your answer. Submit the question the same way you submit any other answer. To practice, use the interactive graphing guide. On each example, press the Watch the steps button to see it done. Then press Try it yourself. Do you use a keyboard or a screen reader? You can type your graph instead. The coordinate grids video and the graphing guide have the steps.

0:00 How to graph your answers: coordinate grids

Some homework questions ask you to answer by drawing on a coordinate grid. Every example in this video uses the same graphing tool as your homework. Pick a tool first, then click the graph. Each tool draws one kind of shape from the points you click. Coordinate grid tools show only a picture, not a name. Watch which picture the pointer clicks in each example. A shape is finished only after its last click. Clicking outside the graph, even on a button, erases a shape you haven't finished. Most graphs move each click to the nearest grid mark, so you don't need to click exactly on a line. Clear All erases everything you drew on that graph. There is no undo. Whenever you need to redraw a graph, click Clear All. It clears only the graph it sits under: a question with two graphs has two Clear All buttons.

0:53 Example 4 · Plot points

Plot the points two comma three, negative four comma one, and zero comma negative five. This question opens with the Line tool selected. Choose the Dot tool first. Click two comma three: from the origin, two right and three up. Click negative four comma one: four left and one up. Click zero comma negative five. It sits on the y axis.

1:21 Example 5 · Graph a line from two points

Graph y equals two x minus three. Find two points on the line. When x equals zero, y equals negative three. When x equals two, y equals two times two minus three equals one. With the Line tool selected, click zero comma negative three. Move to two comma one and click. The line runs through both points to the edges of the graph.

1:47 Example 6 · Graph a linear inequality

Graph y is less than two x plus one. The symbol less than leaves out the boundary, so choose Linear inequality, dashed line. Solid is for less than or equal to, or greater than or equal to. Click two points on the boundary line, y equals two x plus one. Click zero comma one, then one comma three. Move the pointer. The shading follows it. To pick a side, test the point two comma zero. Put x equals two and y equals zero into the inequality. Zero is less than two times two plus one, which is true, so click two comma zero to shade that side. The inequality is finished only after this third click.

2:33 Example 7 · Graph a parabola: vertex first

Graph f of x equals the quantity x minus one, squared, minus four. Choose the Parabola tool. A parabola needs its vertex and one more point. Click the vertex first. For this function, the vertex is one comma negative four. Click one more point on the parabola. f of three equals zero, so click three comma zero. The tool draws the whole parabola.

3:00 Example 8 · Move a point, then remove one

Plot the point two comma three. This graph already has two mistakes on it. The dot at three comma two belongs at two comma three. Choose the Dot tool, the tool that drew it. Press on the dot, drag it to two comma three, and let go. The dot at negative four comma one is extra. Drag it off the graph and let go to remove it. To redraw the whole graph instead, click Clear All. It erases everything so you can start again.

3:32 Keyboard entry instead of drawing

Do you use a keyboard or a screen reader? Is a mouse hard to use? You can type your graph instead of drawing it. From your LMS, start or resume the assignment, then select the More options button at the top of the questions, then User Preferences. Under Drawing Entry, choose Keyboard and text-based drawing entry alternative. Select Update Info, then reload the assignment page. Graph questions now show “Elements to draw:” and an Add new drawing element list in place of the drawing tools.

4:07 Redraw with Clear All

There is no undo. If you need to redraw a graph, click Clear All and draw it again. Your drawing is your answer. Submit the question the same way you submit any other answer. To practice, use the interactive graphing guide. On each example, press the Watch the steps button to see it done. Then press Try it yourself.