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Function A is a linear function. An equation for Function A is 3x+4y=283x + 4y = 28. \newlineWhich of the following functions has the same slope as Function A? \newlineChoices: \newline(A) y=−34x+43y = -\frac{3}{4}x + \frac{4}{3} \newline(B) y=34x−43y = \frac{3}{4}x - \frac{4}{3} \newline(C) y=43x−34y = \frac{4}{3}x - \frac{3}{4} \newline(D) y=−43x+34y = -\frac{4}{3}x + \frac{3}{4}

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Q. Function A is a linear function. An equation for Function A is 3x+4y=283x + 4y = 28. \newlineWhich of the following functions has the same slope as Function A? \newlineChoices: \newline(A) y=−34x+43y = -\frac{3}{4}x + \frac{4}{3} \newline(B) y=34x−43y = \frac{3}{4}x - \frac{4}{3} \newline(C) y=43x−34y = \frac{4}{3}x - \frac{3}{4} \newline(D) y=−43x+34y = -\frac{4}{3}x + \frac{3}{4}
  1. Rewrite equation in slope-intercept form: First, we need to find the slope of Function A by rewriting the equation in slope-intercept form y=mx+by = mx + b, where mm is the slope. So, we solve for yy in 3x+4y=283x + 4y = 28.
  2. Isolate y-term: Subtract 3x3x from both sides to isolate the y-term: 4y=−3x+284y = -3x + 28.
  3. Solve for y: Divide everything by 44 to solve for y: y=−34x+7y = \frac{-3}{4}x + 7.
  4. Identify slope of Function A: Now we know the slope of Function A is −34-\frac{3}{4}. We need to find which of the given choices has the same slope.
  5. Compare slopes with choices: Looking at the choices, we see that (A) y=−34x+43y = -\frac{3}{4}x + \frac{4}{3} has the same slope as Function A, which is −34-\frac{3}{4}.

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