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A line with a slope of −4-4 passes through the points (−1,−6)(-1,-6) and (0,p)(0,p). What is the value of pp?

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Full solution

Q. A line with a slope of −4-4 passes through the points (−1,−6)(-1,-6) and (0,p)(0,p). What is the value of pp?
  1. Given Slope and Point: We are given the slope of the line and a point on the line. We can use the slope formula to find the value of pp. The slope formula is y2−y1x2−x1=slope\frac{y_2 - y_1}{x_2 - x_1} = \text{slope}, where (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) are points on the line.
  2. Apply Slope Formula: We know the slope is −4-4, and we have the points (−1,−6)(-1, -6) and (0,p)(0, p). Let's plug these into the slope formula: −6−p−1−0=−4\frac{-6 - p}{-1 - 0} = -4.
  3. Simplify Equation: Simplify the denominator to get (−6−p)/−1=−4(-6 - p) / -1 = -4.
  4. Isolate Term with pp: Multiply both sides by −1-1 to isolate the term with pp: 6+p=46 + p = 4.
  5. Solve for p: Subtract 66 from both sides to solve for pp: p=4−6p = 4 - 6.
  6. Calculate p Value: Calculate the value of pp: p=−2p = -2.

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