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BIG, IDE:IS MATH 운 #7 i Listen Write a linear function that relates y to x. x 0 1.5 3 4.5 y 5 4 3 2 y= Previous 2 3 4 5 6 7

BIG, IDE:IS MATH\newline운\newline\#77 i\newlineListen\newlineWrite a linear function that relates y y to x x .\newline\begin{tabular}{|c|c|c|c|c|}\newline\hlinex x & 00 & 11.55 & 33 & 44.55 \\\newline\hliney y & 55 & 44 & 33 & 22 \\\newline\hline\newline\end{tabular}\newliney= y= \newlinePrevious\newline22\newline33\newline44\newline55\newline66\newline77

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Q. BIG, IDE:IS MATH\newline운\newline\#77 i\newlineListen\newlineWrite a linear function that relates y y to x x .\newline\begin{tabular}{|c|c|c|c|c|}\newline\hlinex x & 00 & 11.55 & 33 & 44.55 \\\newline\hliney y & 55 & 44 & 33 & 22 \\\newline\hline\newline\end{tabular}\newliney= y= \newlinePrevious\newline22\newline33\newline44\newline55\newline66\newline77
  1. Identify Pattern: Identify the pattern in the xx and yy values.\newlineWe have the following pairs of xx and yy values:\newline(0,5)(0, 5), (1.5,4)(1.5, 4), (3,3)(3, 3), (4.5,2)(4.5, 2)\newlineWe notice that as xx increases by 1.51.5, yy decreases by yy11.
  2. Calculate Slope: Calculate the slope mm of the linear function.\newlineThe slope is the change in yy divided by the change in xx.\newlineUsing the first two points (0,5)(0, 5) and (1.5,4)(1.5, 4), we calculate the slope:\newlinem=y2−y1x2−x1=4−51.5−0=−11.5=−23m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{4 - 5}{1.5 - 0} = -\frac{1}{1.5} = -\frac{2}{3}
  3. Find Y-Intercept: Use the slope and one of the points to find the y-intercept bb. We can use the point (0,5)(0, 5) and the slope −23-\frac{2}{3} in the slope-intercept form of a line, y=mx+by = mx + b. 5=(−23)(0)+b5 = \left(-\frac{2}{3}\right)(0) + b 5=0+b5 = 0 + b b=5b = 5
  4. Write Linear Function: Write the linear function using the slope and y-intercept.\newlineThe linear function is y=mx+by = mx + b.\newlineSubstituting the values of mm and bb, we get:\newliney=(−23)x+5y = \left(-\frac{2}{3}\right)x + 5

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