Math  /  Algebra

Question4. Find the value of kk so that the line passing through (2,3)(2,-3) and (5,k)(5, k) has a slope of 43-\frac{4}{3}.

Studdy Solution

STEP 1

1. The line passes through the points (2,3)(2, -3) and (5,k)(5, k).
2. The slope of the line is 43-\frac{4}{3}.
3. We need to find the value of kk.

STEP 2

1. Recall the formula for the slope of a line.
2. Substitute the given points and slope into the formula.
3. Solve for kk.

STEP 3

Recall the formula for the slope of a line passing through two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2):
m=y2y1x2x1m = \frac{y_2 - y_1}{x_2 - x_1}

STEP 4

Substitute the given points (2,3)(2, -3) and (5,k)(5, k) into the slope formula, and set the slope mm to 43-\frac{4}{3}:
43=k(3)52-\frac{4}{3} = \frac{k - (-3)}{5 - 2}
Simplify the denominator:
43=k+33-\frac{4}{3} = \frac{k + 3}{3}

STEP 5

Solve for kk. Multiply both sides by 3 to eliminate the fraction:
3×43=k+33 \times -\frac{4}{3} = k + 3
Simplify:
4=k+3-4 = k + 3
Subtract 3 from both sides to solve for kk:
k=43k = -4 - 3 k=7k = -7
The value of kk is:
7 \boxed{-7}

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