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The points (3,−8)(3,-8) and (1,r)(1,r) fall on a line with a slope of −3-3. What is the value of rr?\newliner = ____

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Full solution

Q. The points (3,−8)(3,-8) and (1,r)(1,r) fall on a line with a slope of −3-3. What is the value of rr?\newliner = ____
  1. Identify Points: To find the value of rr, we need to use the slope formula, which is (y2−y1)/(x2−x1)=slope(y_2 - y_1) / (x_2 - x_1) = \text{slope}. Here, (x1,y1)(x_1, y_1) is the point (3,−8)(3, -8) and (x2,y2)(x_2, y_2) is the point (1,r)(1, r). The slope is given as −3-3.
  2. Apply Slope Formula: Plugging the values into the slope formula, we get (r−(−8))/(1−3)=−3(r - (-8)) / (1 - 3) = -3. Simplify the equation to find the value of rr.
  3. Simplify Equation: The equation becomes (r+8)/(1−3)=−3(r + 8) / (1 - 3) = -3. Since 1−31 - 3 equals −2-2, the equation simplifies to (r+8)/−2=−3(r + 8) / -2 = -3.
  4. Multiply by −2-2: To solve for rr, we multiply both sides of the equation by −2-2 to get r+8=−3×−2r + 8 = -3 \times -2.
  5. Calculate Result: Calculating the right side of the equation gives us r+8=6r + 8 = 6.
  6. Subtract 88: Finally, we subtract 88 from both sides to solve for rr, which gives us r=6−8r = 6 - 8.
  7. Find Value of r: Calculating the value of rr, we find that r=−2r = -2.

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