Question Video: Finding the Relation between a Given Point and a Straight Line given Its Equation Mathematics • 8th Grade

Video Transcript

What is the relation between the point zero, four and the line 𝑦 equals two 𝑥 minus eight? (A) It lies on the line, (B) it lies above the line, (C) it lies below the line, (D) it is the 𝑦-intercept of the line, or (E) it is the 𝑥-intercept of the line.

We have the equation 𝑦 equals two 𝑥 minus eight and the point zero, four. The first thing we can do is plug in zero, four into 𝑥 and 𝑦 for this equation. We want to know does four equal two times zero minus eight? Two times zero is zero. Zero minus eight is negative eight. Four is not equal to negative eight. Because of that, we can say that this point does not fall on this line as every point that falls along this line when you plug it in will create a true statement.

If we think carefully about this, we can also say something about the 𝑥- and 𝑦-intercept. Because this point does not fall on this line, it cannot be the 𝑥-intercept of the line or the 𝑦-intercept of the line, which means we now need to determine if this point lies above or below the line. To do that, we can sketch a graph of this line in a coordinate plane. When we have a linear equation given in the form 𝑦 equals 𝑚𝑥 plus 𝑏, we know that the 𝑏-value will be the 𝑦-intercept. In our case, that means the 𝑦-intercept is negative eight.

We can plot our first point at zero, negative eight. And because we know our slope is two, we go up two right one for another point, up two right one for another point. And continuing like this, we get an idea of what the line will look like so that we’re able to connect the points and form a line. This is the line 𝑦 equals two 𝑥 minus eight. And we want to add the point zero, four to the graph, which would be here. And when we extend out this line a little bit further, we confirm that the point zero, four is above the line 𝑦 equals two 𝑥 minus eight.

There is one more way to think about this. The point zero, four falls along the 𝑦-axis. It’s the place where 𝑥 equals zero and 𝑦 equals four. In the line 𝑦 equals two 𝑥 minus eight, the 𝑦-intercept, the place where that line crosses the 𝑦-axis, is negative eight. You can imagine that zero, four is above the point on the line zero, negative eight and confirms that the point zero, four is above the line 𝑦 equals two 𝑥 minus eight.