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A line has a slope of 22 and includes the points (2,6)(2,6) and (−1,r)(-1,r). What is the value of rr?\newliner = ____

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Full solution

Q. A line has a slope of 22 and includes the points (2,6)(2,6) and (−1,r)(-1,r). What is the value of rr?\newliner = ____
  1. Given slope and points: We are given the slope of the line m=2m = 2 and two points on the line: (2,6)(2,6) and (−1,r)(-1,r). We can use the slope formula, which is y2−y1x2−x1=m\frac{y_2 - y_1}{x_2 - x_1} = m, where (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) are points on the line and mm is the slope.
  2. Plug in values: Let's plug in the values we know into the slope formula. We'll use (2,6)(2,6) as (x1,y1)(x_1, y_1) and (−1,r)(-1,r) as (x2,y2)(x_2, y_2). So, we have r−6−1−2=2\frac{r - 6}{-1 - 2} = 2.
  3. Solve for r: Now, let's solve for rr. First, simplify the denominator: (−1−2)=−3(-1 - 2) = -3. So, we have r−6−3=2\frac{r - 6}{-3} = 2.
  4. Isolate rr: To isolate rr, we multiply both sides of the equation by −3-3: (r−6)=2×−3(r - 6) = 2 \times -3.
  5. Perform multiplication: Now, perform the multiplication: (r−6)=−6(r - 6) = -6.
  6. Add to solve for rr: Finally, add 66 to both sides to solve for rr: r=−6+6r = -6 + 6.
  7. Add to solve for r: Finally, add 66 to both sides to solve for rr: r=−6+6r = -6 + 6. After adding, we find that r=0r = 0.

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