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A line has a slope of 66 and includes the points (7,6)(7,6) and (5,u)(5,u). What is the value of uu?\newlineu=___u = \_\_\_

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Full solution

Q. A line has a slope of 66 and includes the points (7,6)(7,6) and (5,u)(5,u). What is the value of uu?\newlineu=___u = \_\_\_
  1. Definition 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 any two points on the line. The formula for the slope (mm) between 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. Given Information: We are given the slope of the line m=6m = 6, one point on the line (7,6)(7,6), and the xx-coordinate of another point on the line (5)(5). We need to find the yy-coordinate of this second point, which we are calling uu.
  3. Slope Formula Setup: Using the slope formula with our known point (7,6)(7,6) and our unknown point (5,u)(5,u), we set up the equation 6=(u−6)(5−7)6 = \frac{(u - 6)}{(5 - 7)}.
  4. Eliminating Denominator: Solving for uu, we multiply both sides of the equation by (5−7)(5 - 7), which is −2-2, to get rid of the denominator. This gives us 6×−2=u−66 \times -2 = u - 6.
  5. Calculating Left Side: Now we calculate the left side of the equation: 6×−2=−126 \times -2 = -12. So, −12=u−6-12 = u - 6.
  6. Solving for u: To solve for u, we add 66 to both sides of the equation: −12+6=u−6+6-12 + 6 = u - 6 + 6.
  7. Final Result: This simplifies to −6=u-6 = u. So, the value of uu is −6-6.

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