Question Video: Finding the Unknown Coordinate of a Point That Satisfies a Given Linear Function Mathematics • 8th Grade

Video Transcript

Find the value of 𝑏 given the point two, 𝑏 lies on the straight line 𝑓 of 𝑥 equals negative two 𝑥 plus 10.

We began with our function 𝑓 of 𝑥 equals negative two 𝑥 plus 10. We know that this point two, 𝑏 lies on our line. And something else we have to recognize about this coordinate form two, 𝑏 is that it represents the coordinates 𝑥, 𝑦. Another way to write that is 𝑥 and then 𝑓 of 𝑥, which means that to find 𝑏, we’ll need two and then 𝑓 of two. 𝑏 will be equal to the function at two.

And so, we look at our function and we plug in the value two for 𝑥. Negative two times two is negative four. 𝑓 of two will be equal to negative four plus 10. And that means 𝑓 of two equals six. And since we know that 𝑏 equals 𝑓 of two, 𝑏 equals six. We’re saying that the line passes through the point two, six. For this function, if you input a value of two, the output is six. For the coordinate two, 𝑏, 𝑏 equals six.