Question Video: Graphing Linear Functions by Making Tables Mathematics

Let us consider the function 𝑓(π‘₯) = 8π‘₯ βˆ’ 11. Fill in the table. Identify the three points that lie on the line 𝑦 = 8π‘₯ βˆ’ 11.

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Video Transcript

Let us consider the function 𝑓 of π‘₯ is equal to eight π‘₯ minus 11. Fill in the table. Identify the three points that lie on the line 𝑦 is equal to eight π‘₯ minus 11.

In this question, we are given the linear function 𝑓 of π‘₯ is equal to eight π‘₯ minus 11. The first part of the question asks us to complete the table where we are given π‘₯-values of negative one, zero, and one and need to find the corresponding values of 𝑦 or 𝑓 of π‘₯.

Let’s begin by calculating 𝑓 of negative one. This is equal to eight multiplied by negative one minus 11. And since eight multiplied by negative one is negative eight, 𝑓 of negative one is equal to negative 19. The first missing value in the table is negative 19.

𝑓 of zero is equal to eight multiplied by zero minus 11. This is equal to negative 11. So when π‘₯ is equal to zero, 𝑦 is equal to negative 11. Finally, 𝑓 of one is equal to eight multiplied by one minus 11. This is equal to negative three. When π‘₯ is equal to one, 𝑦 is equal to negative three. The missing values in the table are negative 19, negative 11, and negative three, and the completed table is as shown.

The second part of our question asks us to identify the three points that lie on the line 𝑦 is equal to eight π‘₯ minus 11. From our table, we see that these have coordinates negative one, negative 19; zero, negative 11; and one, negative three. These correspond to point 𝐼, 𝐻, and 𝐺, respectively. Drawing a straight line that passes through these points, we see that it has a positive slope and a 𝑦-intercept equal to negative 11. Since the value of this slope is eight, we can therefore conclude that the three points that lie on the line 𝑦 is equal to eight π‘₯ minus 11 are 𝐼, 𝐻, and 𝐺.

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