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A line with a slope of 33 passes through the points (6,c)(6,c) and (4,−7)(4,-7). What is the value of cc?\newlinec = ____

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Full solution

Q. A line with a slope of 33 passes through the points (6,c)(6,c) and (4,−7)(4,-7). What is the value of cc?\newlinec = ____
  1. Understand problem and formula: Understand the problem and the formula for the slope of a line.\newlineThe slope of a line is given by the formula: slope mm = y2−y1x2−x1\frac{y_2 - y_1}{x_2 - x_1}, where (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) are two points on the line.\newlineWe are given the slope m=3m = 3 and one point (4,−7)(4, -7). We need to find the y-coordinate cc of the other point (6,c)(6, c).
  2. Plug known values into formula: Plug the known values into the slope formula to create an equation.\newlineUsing the slope formula with the given slope m=3m = 3 and the points (6,c)(6, c) and (4,−7)(4, -7), we get:\newline3=c−(−7)6−43 = \frac{c - (-7)}{6 - 4}
  3. Simplify equation and solve: Simplify the equation and solve for cc.3=c+723 = \frac{c + 7}{2}Now, multiply both sides by 22 to isolate cc on one side of the equation:2×3=c+72 \times 3 = c + 76=c+76 = c + 7
  4. Subtract to find value: Subtract 77 from both sides to find the value of cc. \newline6−7=c6 - 7 = c\newline−1=c-1 = c

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