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Function A is a linear function. An equation for Function A is 2y−3=−5x2y - 3 = -5x. Which of the following functions has the same yy-intercept as Function A?\newlineChoices:\newline(A) y=1.5x+2.5y = 1.5x + 2.5\newline(B) y=−1.5x−2.5y = -1.5x - 2.5\newline(C) y=2.5x+1.5y = 2.5x + 1.5\newline(D) y=−2.5x−1.5y = -2.5x - 1.5

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Q. Function A is a linear function. An equation for Function A is 2y−3=−5x2y - 3 = -5x. Which of the following functions has the same yy-intercept as Function A?\newlineChoices:\newline(A) y=1.5x+2.5y = 1.5x + 2.5\newline(B) y=−1.5x−2.5y = -1.5x - 2.5\newline(C) y=2.5x+1.5y = 2.5x + 1.5\newline(D) y=−2.5x−1.5y = -2.5x - 1.5
  1. Find y-intercept of Function A: First, let's find the y-intercept of Function A by getting yy on its own on one side of the equation.2y−3=−5x2y - 3 = -5xAdd 33 to both sides to isolate the 2y2y term.2y=−5x+32y = -5x + 3
  2. Solve for y: Now, divide both sides by 22 to solve for yy.\newliney=−5x+32y = \frac{-5x + 3}{2}\newliney=−2.5x+1.5y = -2.5x + 1.5\newlineThe yy-intercept of Function A is 1.51.5.
  3. Compare y-intercepts: Next, we compare the y-intercept of Function A with the y-intercepts of the given choices.\newline(A) y=1.5x+2.5y = 1.5x + 2.5 has a y-intercept of 2.52.5.\newline(B) y=−1.5x−2.5y = -1.5x - 2.5 has a y-intercept of −2.5-2.5.\newline(C) y=2.5x+1.5y = 2.5x + 1.5 has a y-intercept of 1.51.5.\newline(D) y=−2.5x−1.5y = -2.5x - 1.5 has a y-intercept of −1.5-1.5.
  4. Identify matching function: We see that the y-intercept of Function A 1.51.5 matches the y-intercept of choice (C). So, the function with the same y-intercept as Function A is (C) y=2.5x+1.5y = 2.5x + 1.5.

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