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A line with a slope of −7-7 passes through the points (−7,−4)(-7,-4) and (−9,f)(-9,f). What is the value of ff?\newlinef = ____

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Full solution

Q. A line with a slope of −7-7 passes through the points (−7,−4)(-7,-4) and (−9,f)(-9,f). What is the value of ff?\newlinef = ____
  1. Use Slope Formula: To find the value of ff, we can use the slope formula, which is (change in y)/(change in x)=slope(\text{change in } y) / (\text{change in } x) = \text{slope}. We know the slope is −7-7, and we have the coordinates of one point (−7,−4)(-7, -4) and the xx-coordinate of the second point (−9)(-9). We can set up the equation using the known slope and the coordinates of the first point.
  2. Set Up Equation: Let's denote the coordinates of the first point as (x1,y1)=(−7,−4)(x_1, y_1) = (-7, -4) and the coordinates of the second point as (x2,y2)=(−9,f)(x_2, y_2) = (-9, f). The slope formula is y2−y1x2−x1=slope\frac{y_2 - y_1}{x_2 - x_1} = \text{slope}. Plugging in the known values, we get f−(−4)−9−(−7)=−7\frac{f - (-4)}{-9 - (-7)} = -7.
  3. Simplify Equation: Simplify the equation: (f+4)/(−9+7)=−7(f + 4) / (-9 + 7) = -7. This simplifies to (f+4)/(−2)=−7(f + 4) / (-2) = -7.
  4. Multiply Both Sides: To find ff, we multiply both sides of the equation by −2-2: f+4=−7×−2f + 4 = -7 \times -2.
  5. Calculate Right Side: Calculate the right side of the equation: f+4=14f + 4 = 14.
  6. Subtract 44: Subtract 44 from both sides to solve for ff: f=14−4f = 14 - 4.
  7. Calculate Final Value: Calculate the final value of ff: f=10f = 10.

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