A vendor has learned that, by pricing carmel apples at 1.50 , sales will reach 127 carmel apples per day. Raising the price to 2.50 will cause the sales to fall to 87 carmel apples per day. Let y be the number of carmel apples the vendor sells at x dollars each. Find a linear equation that models the number of carmel apples sold per day when the price is x dollars each. Write the equation in slope-intercept form using function notation.

<p> <br />1. We were given two points based on the sales of caramel apples at different prices: \( (1.50, 127) \) and \( (2.50, 87) \).<br />2. Using these points, we calculated the slope of the line representing the relationship between price and sales. The formula for slope is \( m = \frac{y_2 - y_1}{x_2 - x_1} \). Using the given points, the slope was found to be -40.<br />3. With the slope known, we used the point-slope form of a linear equation to express the relationship: \( y - y_1 = m(x - x_1) \). Substituting in the known values, we got \( y - 127 = -40(x - 1.50) \).<br />4. Finally, we rearranged this equation to the slope-intercept form \( y = mx + b \). Using one of the given points, we solved for the y-intercept \( b \) and found it to be 187. Thus, the equation that models the number of caramel apples sold per day when the price is \( x \) dollars each is \( f(x) = -40x + 187 \).<br /></p>