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A line with a slope of 1010 passes through the points (7,d)(7,d) and (6,−1)(6,-1). What is the value of dd?\newlined = ____

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Q. A line with a slope of 1010 passes through the points (7,d)(7,d) and (6,−1)(6,-1). 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) is given by: m=(y2−y1)(x2−x1)m = \frac{(y_2 - y_1)}{(x_2 - x_1)} Here, we are given the slope (mm) as 1010, and we have two points (7,d)(7, d) and (6,−1)(6, -1).
  2. Plug values into formula: Plug the known values into the slope formula.\newlineUsing the given slope and points, we can set up the equation:\newline10=d−(−1)7−610 = \frac{d - (-1)}{7 - 6}
  3. Simplify equation: Simplify the equation. 10=(d+1)110 = \frac{(d + 1)}{1}
  4. Solve for d: Solve for d.\newlineTo find d, we multiply both sides of the equation by 11 (which doesn't change anything since it's the multiplicative identity):\newline10×1=d+110 \times 1 = d + 1\newline10=d+110 = d + 1
  5. Isolate variable dd: Subtract 11 from both sides to isolate dd.10−1=d10 - 1 = d9=d9 = d

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