1. Drawing a linehttps://peda.net/id/1a838fba2cf2022-09-05T12:42:41+03:00https://peda.net/:static/533/peda.net.logo.bg.svg<div class="license">Tämän sivun lisenssi <a rel="license" href="https://peda.net/info">Peda.net-yleislisenssi</a></div>
Drawing a linehttps://peda.net/id/1a8aeb142cf2020-11-24T19:04:46+02:00<p class="p1">A <b>line</b> that is drawn in a coordinate system can be described with an <b>equation</b>. The equation of a line indicates how the <em>[[$ x $]]</em> and <em>[[$ y $]] </em>coordinates of the points that make up the line depend on one another. To draw a line, you must know at least two points on the line. Usually, three points are required to draw a line, with one of the points serving as a checkpoint.</p>
<div class="eoppi-summary">
<h3><b>Instructions for drawing a line</b></h3>
<ol>
<li>Choose three suitable values of [[$ x $]].</li>
<li>Calculate and table the corresponding values of [[$ y $]].</li>
<li>Draw a coordinate system and mark the points ([[$ x $]], [[$ y $]]) on it.</li>
<li>Draw the line through the points.</li>
<li>Write the equation next to the line.</li>
</ol>
</div>
<h3><b><br/>
Example 1</b></h3>
<p class="p1">Draw the graph of the line <b> </b>[[$ y = 2x $]].</p>
<span class="right medium"><a href="https://peda.net/qis/2022-2023/mathematics/matematiikka-8/oisjv/1sp/suoran-piirt%C3%A4minen/s2k1#top" title="1_coordinates-line-example1.png"><img src="https://peda.net/qis/2022-2023/mathematics/matematiikka-8/oisjv/1sp/suoran-piirt%C3%A4minen/s2k1:file/photo/5d43be14cc92b3a99b90ad412d2e768d16ee24c6/1_coordinates-line-example1.png" alt="" title="Example 1" class="inline" loading="lazy"/></a></span>
<p class="p1"><b>Solution:</b> First, calculate some values of <em>[[$ y $]] </em>with some values of <em>[[$ x $]]</em>. You can choose any number as the value of <em>[[$ x $]],</em> but it is usually best to use small numbers. When using small numbers, it will be easier to calculate the values of [[$ y $]] and place the points in the coordinate system.</p>
<table>
<tbody>
<tr>
<td>[[$ x $]]</td>
<td>[[$ y = 2x $]]</td>
<td>[[$ (x, y) $]]</td>
</tr>
<tr>
<td>[[$ 0 $]]</td>
<td>[[$ 2 \cdot 0 = 0 $]] </td>
<td>[[$ (0, 0) $]]</td>
</tr>
<tr>
<td>[[$ 1 $]]</td>
<td>[[$ 2 \cdot 1 = 2 $]]</td>
<td>[[$ (1, 2) $]]</td>
</tr>
<tr>
<td>[[$ 2 $]]</td>
<td>[[$ 2 \cdot 2 = 4 $]]</td>
<td>[[$ (2, 4) $]]</td>
</tr>
</tbody>
</table>
<p class="p1">Mark the points in the coordinate system and draw a line through them. Write the equation that describes the line next to it.</p>
<h3><b>Example 2</b></h3>
<p class="p1">Draw the lines [[$ y=4 $]] and [[$ x=\:–3 $]] in the same coordinate system.<span class="right medium"><a href="https://peda.net/qis/2022-2023/mathematics/matematiikka-8/oisjv/1sp/suoran-piirt%C3%A4minen/s2k12#top" title="1_coordinates-line-example2.png"><img src="https://peda.net/qis/2022-2023/mathematics/matematiikka-8/oisjv/1sp/suoran-piirt%C3%A4minen/s2k12:file/photo/347a1b22da46ab3cd2359b4795ae7c8fdfd64550/1_coordinates-line-example2.png" alt="" title="Example 2" class="inline" loading="lazy"/></a></span></p>
<table border="1">
<tbody>
<tr>
<th class="center">[[$ x $]]</th>
<th class="center">[[$ y = 4 $]]</th>
<td>There is no [[$ x $]] in the [[$ y $]]-equation.</td>
</tr>
<tr>
<td class="center">[[$ -1 $]]</td>
<td class="center">[[$ 4 $]]</td>
<td rowspan="3">The [[$ x $]]-coordinate can be given any value, <br/>
but the [[$ y $]]-coordinate is always 4.</td>
</tr>
<tr>
<td class="center">[[$ 0 $]]</td>
<td class="center">[[$ 4 $]]</td>
</tr>
<tr>
<td class="center">[[$ 1 $]]</td>
<td class="center">[[$ 4 $]]</td>
</tr>
</tbody>
</table>
<p class="p1"> </p>
<table border="1">
<tbody>
<tr>
<th class="center">[[$ y $]]</th>
<th class="center">[[$ x = -3 $]]</th>
<td>There is no [[$ y $]] in the [[$ x $]]-equation.</td>
</tr>
<tr>
<td class="center">[[$ -1 $]]</td>
<td class="center">[[$ -3 $]]</td>
<td rowspan="3">The [[$ y $]]-coordinate can be given any value, <br/>
but the [[$ x $]]-coordinate is a<span>lways -3.</span></td>
</tr>
<tr>
<td class="center">[[$ 0 $]]</td>
<td class="center">[[$ -3 $]]</td>
</tr>
<tr>
<td class="center">[[$ 1 $]]</td>
<td class="center">[[$ -3 $]]</td>
</tr>
</tbody>
</table>
<p class="p1"><span> </span></p>
<div class="eoppi-summary">
<h3><b>Lines parallel to the coordinate axes</b></h3>
The graphs of lines that have the form [[$y=$]] are parallel to the [[$x$]]-axis.<br/>
The graphs of lines that have the form [[$x=$]] are parallel to the [[$y$]]-axis.</div>
2022-09-05T12:42:41+03:00Exerciseshttps://peda.net/id/1a8c811b2cf2020-06-07T13:11:42+03:00<a href="https://peda.net/id/1a8d859f2cf" rel="noopener" target="_blank">Basic exercises<br/>
</a><a href="https://peda.net/id/1a92612a2cf" rel="noopener" target="_blank">Applied exercises<br/>
</a><a href="https://peda.net/id/1a961faa2cf" rel="noopener" target="_blank">Challenging exercises</a>2022-09-05T12:42:41+03:00