Video Transcript
Find the values of π and π given the function π of π₯ equals negative 14π₯ plus π intersects the π¦-axis at the point π, negative three.
We have the function π of π₯ is equal to negative 14π₯ plus π and the point along this line π, negative three. Weβve been told that this point intersects the π¦-axis. On a coordinate grid, the point at which a function intersects the π¦-axis is the π¦-intercept. And the π¦-intercept is always located at the point zero, π, where π is some constant value for π¦. If we know that the π¦-intercept is located at zero, π, then we can say something about the point π, negative three. We can say that π must be equal to zero. And then we can use the point zero, negative three to solve for our missing variable π.
By plugging in zero for π₯ and negative three for π of π₯, we see that negative three must be equal to π as negative 14 times zero equals zero, which makes our function π of π₯ is equal to negative 14π₯ minus three. And it means we found that π equals negative three and π equals zero.
Itβs also worth pointing out that for an equation in the form π¦ equals ππ₯ plus π, π is the constant value of the π¦-intercept. And as we had an equation for the π¦-intercept zero, π, where π was equal to negative three, we can plug that value directly in for π. π must be equal to negative three as it is the π¦-coordinate of the π¦-intercept of this function. And π must be equal to zero because it is the π₯-coordinate of the π¦-intercept of this function.