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The points (5,−10)(5,-10) and (7,w)(7,w) fall on a line with a slope of 66. What is the value of ww?\newlinew=___w = \_\_\_

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Full solution

Q. The points (5,−10)(5,-10) and (7,w)(7,w) fall on a line with a slope of 66. What is the value of ww?\newlinew=___w = \_\_\_
  1. Use Slope Formula: To find the value of ww, we can use the slope formula, which is (y2−y1)/(x2−x1)=slope(y_2 - y_1) / (x_2 - x_1) = \text{slope}, where (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) are the coordinates of two points on the line. We know the slope is 66, and we have the points (5,−10)(5, -10) and (7,w)(7, w).
  2. Plug in Values: Let's plug in the values into the slope formula: w−(−10)7−5=6\frac{w - (-10)}{7 - 5} = 6. This simplifies to w+102=6\frac{w + 10}{2} = 6.
  3. Isolate w: Now, we multiply both sides of the equation by 22 to isolate ww on one side: 2×(w+102)=2×62 \times \left(\frac{w + 10}{2}\right) = 2 \times 6.
  4. Subtract 1010: This simplifies to w+10=12w + 10 = 12. Now, we just need to subtract 1010 from both sides to find the value of ww.
  5. Calculate ww: Subtracting 1010 from both sides gives us w=12−10w = 12 - 10.
  6. Calculate ww: Subtracting 1010 from both sides gives us w=12−10w = 12 - 10. Calculating the subtraction, we find that w=2w = 2.

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