### Video Transcript

Write the equation that represents the linear function shown in the given table.

Since we know that this is a linear function โ that is, itโs a straight line function โ we know that ๐ฆ equals ๐๐ฅ plus ๐ is a general form of a linear function. And to find an equation, we need to know two things. We need the slope and the ๐ฆ-intercept. And the ๐-value, the slope, can be found as long as you have two points along the line. If you have two points, you can say ๐ฆ two minus ๐ฆ one over ๐ฅ two minus ๐ฅ one is the slope.

And finally, we know that the ๐ฆ-intercept is where ๐ฅ equals zero. Bringing this information to the table, we see that when ๐ฅ equals zero, ๐ฆ equals five. The point zero, five falls on this line. And we can plug in the value five for ๐. Five is the ๐ฆ-intercept. We can list the other coordinates โ negative two, three and negative one, four.

Remember that I said we just need two points to find the slope. We could use negative two, three; negative one, four. Or we could use negative one, four and zero, five or even negative two, three and zero, five. Any combination of these three points will work. Letโs say we take the first two. Weโll let the first point be ๐ฅ one, ๐ฆ one and the second point be ๐ฅ two, ๐ฆ two. Then the slope will be four minus three over negative one minus negative two. Four minus three is one. Negative one minus negative two is negative one plus two, which is one.

And so, we can say that the slope of this line is one. And ๐ฆ will be equal to one times ๐ฅ plus five, which we can simplify to be ๐ฆ equals ๐ฅ plus five. Now that we have this equation, letโs double-check it against the table. If we plug in negative two, negative two plus five does equal three. Negative one plus five does equal four. And zero plus five does equal five. Which confirms that we have found the correct linear function equation, ๐ฆ equals ๐ฅ plus five.