Video: Finding the Slope of a Linear Function given a Function Table

What is the slope of the linear function represented by the given table?

02:52

Video Transcript

What is the slope of the linear function represented by the given table?

We know that the equation of any linear function is written in the form 𝑦 equals π‘šπ‘₯ plus 𝑏, where π‘š is the slope or gradient of the function and 𝑏 is the 𝑦-intercept. We can calculate the value of the slope π‘š using the following formula, 𝑦 two minus 𝑦 one over π‘₯ two minus π‘₯ one. This is the change in 𝑦-coordinates over the change in π‘₯-coordinates, where any two points 𝐴 and 𝐡 have coordinates π‘₯ one, 𝑦 one and π‘₯ two, 𝑦 two, respectively.

In our table, we have three coordinates, firstly, zero, four. Our second coordinate has an π‘₯-value of two and a 𝑦-value of 10. Our third coordinate, which we will call 𝐢, is four, 16. We can select any two of these three coordinates. In this question, we will begin by considering point 𝐴 and point 𝐡. The 𝑦-coordinates of these two points are 10 and four. The corresponding π‘₯-coordinates are two and zero. The slope π‘š is equal to 10 minus four over two minus zero. This simplifies to six over two, giving us a final answer of a slope of three.

We can check this answer by selecting a different two points, in this case point 𝐴 and point 𝐢. This time the slope is equal to 16 minus four over four minus zero. 12 divided by four is also equal to three. We would get the same answer if we use the points 𝐡 and 𝐢. The slope of the linear function represented by the table is three.

We could also calculate this answer just by looking at the table. The change in π‘₯-values between the first and second point is plus two. The change in the 𝑦-values between the first two points is plus six. As the slope is equal to the change in 𝑦-values divided by the change in π‘₯-values, this also gives us an answer of three. For each single unit the π‘₯-value increases, the 𝑦-value will increase by three units.

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