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