Rule of correspondence question.

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To find the rule of correspondence for the linear function containing the points (3, -1) and (2, 3), the slope must first be calculated. The slope is determined by the change in y over the change in x, leading to the equation f(x) = -4x + 11. Using the point-slope form, y - y0 = m(x - x0), allows for the equation to be derived from either point. This method confirms that the choice of point does not affect the final equation. Understanding these steps is essential for determining the equation of a line from two given points.
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Homework Statement


find a rule of correspondence for the linear function f whose graph contains the given points.

(3, -1) and (2, 3)

Homework Equations





The Attempt at a Solution



would you try to find the slope first and then after finding that I'm unsure of what to do.




the answer is f(x)= -4x + 11
 
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There are several ways of determining the equation of a line. The method you choose depends on what information you have. In this case, you're given two points, so you could find the slope. Now the easiest way to find the equation is to use the point-slope form.

y-y_0 = m(x-x_0)

Just choose one of the points to use as (x0, y0) and plug your slope in and simplify. You might want to try it with both points to see that it doesn't make a difference which one you choose.
 
thanks.
 

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