Question Video: Finding the Unknown in a Problem Involving a Point Satisfying a Given Relation

Video Transcript

Given that one, 𝑎 satisfies the relation 𝑦 minus four 𝑥 equals seven, find the value of 𝑎.

We have the relationship 𝑦 minus four 𝑥 equals seven, and we’re told that the coordinate one, 𝑎 satisfies this relationship. If we plug in one, 𝑎, the statement will be true. This coordinate form is 𝑥 and then 𝑦. And that means in this equation, we’ll plug in one for 𝑥 and 𝑎 for 𝑦. We’ll bring everything else down and have a statement that says 𝑎 minus four times one equals seven.

To solve for this, first, we’ll multiply four times one, which is four. We’ll then have 𝑎 minus four equals seven. To isolate 𝑎, we add four to both sides of the equation, and we get that 𝑎 equals 11. This means that the coordinate one, 11 satisfies this equation.

We might wanna quickly check and see if that’s true, where we ask, is 11 minus four times one equal to seven? 11 minus four does equal seven, which confirms the coordinates one, 11. And so, the 𝑎-value is 11.