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A line that includes the points (−4,−3)(-4,-3) and (−3,z)(-3,z) has a slope of 88. What is the value of zz?\newlinez = ____

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Full solution

Q. A line that includes the points (−4,−3)(-4,-3) and (−3,z)(-3,z) has a slope of 88. What is the value of zz?\newlinez = ____
  1. Identify Points and Slope: Identify the given points and the slope.\newlineWe have the points (−4,−3)(-4, -3) and (−3,z)(-3, z) and the slope of the line is 88.
  2. Use Slope Formula: Use the slope formula to set up the equation.\newlineThe slope formula is (y2−y1)/(x2−x1)(y_2 - y_1) / (x_2 - x_1). Here, we have slope m=8m = 8, y2=zy_2 = z, y1=−3y_1 = -3, x2=−3x_2 = -3, and x1=−4x_1 = -4.\newlineSo, 8=(z−(−3))/(−3−(−4))8 = (z - (-3)) / (-3 - (-4)).
  3. Simplify Equation: Simplify the equation.\newline8=z+3−3+48 = \frac{z + 3}{-3 + 4}.\newline8=z+318 = \frac{z + 3}{1}.
  4. Solve for z: Solve for z.\newlineMultiply both sides by 11 to isolate zz.\newline8×1=z+38 \times 1 = z + 3.\newline8=z+38 = z + 3.
  5. Subtract to Find zz: Subtract 33 from both sides to find the value of zz.8−3=z+3−38 - 3 = z + 3 - 3.5=z5 = z.

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