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A line with a slope of 88 passes through the points (−3,5)(-3,5) and (−4,k)(-4,k). What is the value of kk?\newlinek = ____

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Full solution

Q. A line with a slope of 88 passes through the points (−3,5)(-3,5) and (−4,k)(-4,k). What is the value of kk?\newlinek = ____
  1. Given Information: We are given the slope of the line and one point on the line. We can use the slope formula to find the value of kk. The slope formula is (y2−y1)/(x2−x1)=(y_2 - y_1) / (x_2 - x_1) = slope, where (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) are points on the line.
  2. Slope Formula: Let's plug in the values we know into the slope formula. We have the slope 88, one point (−3,5)(-3,5), and the x-coordinate of the second point (−4)(-4). We are looking for the y-coordinate of the second point, which is kk. So, we have k−5−4−(−3)=8\frac{k - 5}{-4 - (-3)} = 8.
  3. Plug in Values: Simplify the denominator of the slope formula. We have −4−(−3)-4 - (-3) which simplifies to −4+3-4 + 3, which equals −1-1. So, our equation now looks like (k−5)/−1=8(k - 5) / -1 = 8.
  4. Simplify Denominator: Now, we solve for kk. Multiply both sides of the equation by −1-1 to get k−5=−8k - 5 = -8.
  5. Solve for kk: Finally, add 55 to both sides of the equation to isolate kk. We get k=−8+5k = -8 + 5, which simplifies to k=−3k = -3.

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