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A line with a slope of −10-10 passes through the points (4,10)(4,10) and (6,d)(6,d). What is the value of dd?\newlined = ____

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Q. A line with a slope of −10-10 passes through the points (4,10)(4,10) and (6,d)(6,d). What is the value of dd?\newlined = ____
  1. Understand slope concept: Understand the concept of slope. The slope of a line is the ratio of the change in the yy-coordinate to the change in the xx-coordinate between two points on the line. The formula for slope (mm) when given two points ((x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2)) is: m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}
  2. Apply slope formula: Apply the slope formula to the given points and slope.\newlineWe know the slope mm is −10-10, and we have the points (4,10)(4,10) and (6,d)(6,d). Let's plug these values into the slope formula:\newline−10=d−106−4-10 = \frac{d - 10}{6 - 4}
  3. Solve for d: Solve for d.\newlineNow we need to solve the equation for d:\newline−10=(d−10)2-10 = \frac{(d - 10)}{2}\newlineMultiply both sides by 22 to isolate (d−10)(d - 10):\newline−10×2=d−10-10 \times 2 = d - 10\newline−20=d−10-20 = d - 10\newlineNow, add 1010 to both sides to solve for d:\newline−20+10=d-20 + 10 = d\newline−10=d-10 = d

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