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A line with a slope of −9-9 passes through the points (−9,1)(-9,1) and (−10,q)(-10,q). What is the value of qq?\newlineq = ____

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Full solution

Q. A line with a slope of −9-9 passes through the points (−9,1)(-9,1) and (−10,q)(-10,q). What is the value of qq?\newlineq = ____
  1. Calculate Slope Formula: The slope of a line is calculated using the formula (change in y)/(change in x)(\text{change in } y) / (\text{change in } x), which is also known as rise over run. We can use the coordinates of the two points (−9,1)(-9,1) and (−10,q)(-10,q) to find the value of qq.
  2. Set Up Equation: The slope between the two points is given as −9-9. We can set up the equation using the slope formula:\newlineSlope mm = y2−y1x2−x1\frac{y_2 - y_1}{x_2 - x_1}\newlineHere, (x1,y1)=(−9,1)(x_1, y_1) = (-9, 1) and (x2,y2)=(−10,q)(x_2, y_2) = (-10, q). Plugging these values into the formula gives us:\newline−9=q−1−10−(−9)-9 = \frac{q - 1}{-10 - (-9)}
  3. Simplify Denominator: Simplify the denominator of the slope equation:\newline−9=q−1−10+9-9 = \frac{q - 1}{-10 + 9}\newline−9=q−1−1-9 = \frac{q - 1}{-1}
  4. Multiply by −1-1: To find the value of qq, we multiply both sides of the equation by −1-1:\-9 \times (-1) = (q - 1) \times (-1) / (-1)9=q−19 = q - 1
  5. Add 11 to Solve: Now, we add 11 to both sides of the equation to solve for qq: \newline9+1=q−1+19 + 1 = q - 1 + 1\newline10=q10 = q

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