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The points (6,s)(6,s) and (4,−10)(4,-10) fall on a line with a slope of 66. What is the value of ss?\newlines = ____

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Full solution

Q. The points (6,s)(6,s) and (4,−10)(4,-10) fall on a line with a slope of 66. What is the value of ss?\newlines = ____
  1. Slope Formula: We know the formula for the slope mm between two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) is given by:\newlinem=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}\newlineWe are given the slope m=6m = 6, one point (4,−10)(4, -10), and the x-coordinate of the second point (6)(6). We need to find the y-coordinate of the second point, which is ss.
  2. Plug in Values: Let's plug in the values into the slope formula: 6=s−(−10)6−46 = \frac{s - (-10)}{6 - 4}
  3. Simplify Equation: Simplify the equation: 6=s+1026 = \frac{s + 10}{2}
  4. Isolate ss: Multiply both sides by 22 to isolate ss on one side:\newline2×6=s+102 \times 6 = s + 10
  5. Calculate Left Side: Calculate the left side of the equation: 12=s+1012 = s + 10
  6. Subtract 1010: Subtract 1010 from both sides to solve for ss: \newlines=12−10s = 12 - 10
  7. Final Value of s: Calculate the final value of s: s=2s = 2

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