Video: Determining the Graph of a Linear Function by Making a Table of Values

By making a table of values, determine which of the following graphs represents the equation 𝑦 = 1/2π‘₯ + 1. [A] Graph A [B] Graph B [C] Graph C [D] Graph D [E] Graph E

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Video Transcript

By making a table of values, determine which of the following graphs represents the equation 𝑦 equals a half π‘₯ plus one.

In this question, we’re asked to make a table of values. This can be a very useful tool to help us draw the graphs of functions. Setting up a table of π‘₯- and 𝑦-values will give us sets of coordinates that will lie on the graph. So which π‘₯-values do we choose then? Well, we can see that all of our graph options roughly go from π‘₯ is negative four up to π‘₯ is four. So choosing a few values within this range would be a sensible option.

In order to find the 𝑦-value for each π‘₯-value, we substitute into the equation 𝑦 equals a half π‘₯ plus one. So when π‘₯ is negative two, we have 𝑦 equals a half times negative two plus one. And a half times negative two will give us negative one. So we have 𝑦 equals negative one plus one, which is zero. And so we found that when π‘₯ is negative two, 𝑦 is equal to zero. When π‘₯ is equal to negative one, we have 𝑦 equals a half times negative one plus one. And a half times negative one is negative a half plus one. And so we found another pair of values in the table.

We can continue to complete the values in the table. When we have completed the table of values, we will be able to identify coordinates which lie on the line. Taking the first set of coordinates of negative two, zero, we can see that only graphs C and E have this coordinate on the line. Identifying the second coordinate of negative one, a half, on graph C, we can see that this will be negative one, negative a half, meaning that we can rule out option C. We can confirm that graph E does go through the coordinate negative one, a half. It also goes through the coordinate zero, one; one, three over two; and two, two. Therefore, the graph given in E represents the equation 𝑦 equals a half π‘₯ plus one.

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