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A line that includes the points (1,−1)(1,-1) and (3,k)(3,k) has a slope of 33. What is the value of kk?\newlinek = ____

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Full solution

Q. A line that includes the points (1,−1)(1,-1) and (3,k)(3,k) has a slope of 33. What is the value of kk?\newlinek = ____
  1. Calculate Slope: To find the value of kk, we need to use the formula for the slope of a line, which is (change in yy) / (change in xx). The slope is given as 33, and we have the points (1,−1)(1, -1) and (3,k)(3, k).\newlineSlope formula: (y2−y1)/(x2−x1)=(y_2 - y_1) / (x_2 - x_1) = slope\newlineHere, (x1,y1)=(1,−1)(x_1, y_1) = (1, -1) and (x2,y2)=(3,k)(x_2, y_2) = (3, k).
  2. Apply Slope Formula: Plugging the values into the slope formula, we get:\newline(k−(−1))/(3−1)=3(k - (-1)) / (3 - 1) = 3\newlineSimplify the equation:\newline(k+1)/2=3(k + 1) / 2 = 3
  3. Solve for k: To find the value of kk, we need to solve for kk. Multiply both sides of the equation by 22 to get rid of the denominator:\newline2×(k+12)=2×32 \times \left(\frac{k + 1}{2}\right) = 2 \times 3
  4. Isolate kk: Simplifying the equation, we get: k+1=6k + 1 = 6
  5. Final Value of k: Subtract 11 from both sides to isolate kk:\newlinek+1−1=6−1k + 1 - 1 = 6 - 1\newlinek=5k = 5

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