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The points (1,4)(1,4) and (2,q)(2,q) fall on a line with a slope of −9-9. What is the value of qq?\newlineq = ____

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Full solution

Q. The points (1,4)(1,4) and (2,q)(2,q) fall on a line with a slope of −9-9. What is the value of qq?\newlineq = ____
  1. Identify Points and Slope: Identify the given points and the slope.\newlineWe have the points (1,4)(1, 4) and (2,q)(2, q) and the slope of the line is −9-9.
  2. Set Up Equation: Use the slope formula to set up an equation.\newlineThe slope formula is (y2−y1)/(x2−x1)(y_2 - y_1) / (x_2 - x_1). Here, (x1,y1)=(1,4)(x_1, y_1) = (1, 4) and (x2,y2)=(2,q)(x_2, y_2) = (2, q). The slope is −9-9.\newlineSo, −9=(q−4)/(2−1)-9 = (q - 4) / (2 - 1).
  3. Solve for q: Solve the equation for q.\newline−9=q−41-9 = \frac{q - 4}{1}\newlineMultiply both sides by 11 to get rid of the denominator.\newline−9×1=q−4-9 \times 1 = q - 4\newline−9=q−4-9 = q - 4
  4. Isolate q: Add 44 to both sides to isolate qq. \newline−9+4=q−4+4-9 + 4 = q - 4 + 4\newline−5=q-5 = q

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