# Question Video: Finding the Value of the Unknown Coefficients of a Linear Function given Its π¦-Intercept and Its Value at a Certain π₯ Value

Find π and π, given π(π₯) = ππ₯ + π, where π(11) = 163 and the function intersects the π¦-axis at the point (0, β24).

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### Video Transcript

Find π and π given that π of π₯ equals ππ₯ plus π, where π of 11 is equal to 163 and the function intersects the π¦-axis at the point zero, negative 24.

Letβs think about what we know. Weβre working with a function in the form π of π₯ equals ππ₯ plus π. We know that π of 11 is equal to 163. And we also know that this function intersects the π¦-axis at the point zero, negative 24. We should recognize that the function weβre working with, π of π₯ equals ππ₯ plus π, looks very similar to the form π¦ equals ππ₯ plus π. In the form π¦ equals ππ₯ plus π, the π-value is the slope of the function and the π-value will be equal to the π¦-intercept, where the function intersects the π¦-axis. And itβs always located at the point zero, π.

Looking at our equation, the π-value will be equal to the slope and the π-value will be equal to the π¦-intercept. If we know two points, we calculate the slope by saying π¦ two minus π¦ one over π₯ two minus π₯ one. At first, it might not seem like we have two points. However, we can rewrite this π of 11 equals 163 into coordinate form. When π₯ equals 11, π of π₯ equals 163. From there, we can label these points π₯ one, π¦ one; π₯ two, π¦ two. And that means our π-value will be equal to negative 24 minus 163 over zero minus 11.

Negative 187 over negative 11 equals positive 17. And that means our π-value is equal to 17. The key to finding our π-value is to recognize that the π-value is the π¦-intercept. And weβve been given the π¦-intercept. Since we know this function crosses the point zero, negative 24, the π¦-intercept, π, must be equal to negative 24. Our function would look like this. π of π₯ is equal to 17π₯ minus 24, where π equals 17 and π equals negative 24.