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A line that includes the points (−9,−1)(-9,-1) and (−8,p)(-8,p) has a slope of 1010. What is the value of pp?\newlinep = ____

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Full solution

Q. A line that includes the points (−9,−1)(-9,-1) and (−8,p)(-8,p) has a slope of 1010. What is the value of pp?\newlinep = ____
  1. Identify Points and Slope: Identify the given points and the slope.\newlineWe have the points (−9,−1)(-9, -1) and (−8,p)(-8, p) and the slope of the line is given as 1010.\newlineWe will use the slope formula which is (y2−y1)/(x2−x1)=slope.(y_2 - y_1) / (x_2 - x_1) = \text{slope}.
  2. Plug Values into Formula: Plug the values into the slope formula.\newlineUsing the points (−9,−1)(-9, -1) as (x1,y1)(x_1, y_1) and (−8,p)(-8, p) as (x2,y2)(x_2, y_2), we get:\newline10=p−(−1)−8−(−9)10 = \frac{p - (-1)}{-8 - (-9)}
  3. Simplify the Equation: Simplify the equation.\newline10=p+1−8+910 = \frac{p + 1}{-8 + 9}\newline10=p+1110 = \frac{p + 1}{1}
  4. Solve for p: Solve for p.\newlineMultiply both sides by 11 to isolate pp.\newline10×1=(p+1)10 \times 1 = (p + 1)\newline10=p+110 = p + 1
  5. Subtract to Find pp: Subtract 11 from both sides to find the value of pp.10−1=p+1−110 - 1 = p + 1 - 19=p9 = p

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