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A line with a slope of −3-3 passes through the points (−5,f)(-5,f) and (−4,−3)(-4,-3). What is the value of ff?\newlinef = ____

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Q. A line with a slope of −3-3 passes through the points (−5,f)(-5,f) and (−4,−3)(-4,-3). What is the value of ff?\newlinef = ____
  1. Understand slope concept: Understand the concept of slope. The slope of a line is the ratio of the change in the yy-coordinate to the change in the xx-coordinate between two points on the line. The formula for slope (mm) is given by: m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1} In this problem, we are given the slope (m=−3m = -3) and two points ((−5,f)(-5, f)) and ((−4,−3)(-4, -3)).
  2. Substitute values into formula: Substitute the given values into the slope formula.\newlineWe have m=−3m = -3, x1=−5x_1 = -5, y1=fy_1 = f, x2=−4x_2 = -4, and y2=−3y_2 = -3. Plugging these into the slope formula gives us:\newline−3=−3−f−4−(−5)-3 = \frac{-3 - f}{-4 - (-5)}
  3. Simplify denominator: Simplify the denominator of the fraction.\newline−4−(−5)-4 - (-5) simplifies to −4+5-4 + 5, which equals 11. So the equation becomes:\newline−3=−3−f1-3 = \frac{-3 - f}{1}
  4. Multiply by denominator: Multiply both sides of the equation by the denominator to solve for ff. Multiplying both sides by 11 does not change the equation, so we have: −3=−3−f-3 = -3 - f
  5. Add to isolate ff: Add 33 to both sides of the equation to isolate ff.\newline−3+3=−3+3−f-3 + 3 = -3 + 3 - f\newline0=0−f0 = 0 - f
  6. Simplify to find ff: Simplify the equation to find the value of ff.0=−f0 = -fMultiplying both sides by −1-1 gives us:0×−1=−f×−10 \times -1 = -f \times -10=f0 = f

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