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A line with a slope of −6-6 passes through the points (4,−2)(4,-2) and (2,h)(2,h). What is the value of hh?

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Full solution

Q. A line with a slope of −6-6 passes through the points (4,−2)(4,-2) and (2,h)(2,h). What is the value of hh?
  1. Understand slope concept: Understand the concept of slope. The slope of a line is the ratio of the change in the yy-coordinate to the change in the xx-coordinate between two points on the line. The formula for slope (mm) when given two points ((x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2)) is: m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}
  2. Apply slope formula: Apply the slope formula to the given points and slope.\newlineWe know the slope mm is −6-6, and we have the points (4,−2)(4, -2) and (2,h)(2, h). Let's plug these values into the slope formula:\newline−6=h−(−2)2−4-6 = \frac{h - (-2)}{2 - 4}
  3. Simplify equation and solve: Simplify the equation and solve for hh.−6=h+22−4-6 = \frac{h + 2}{2 - 4}−6=h+2−2-6 = \frac{h + 2}{-2}Now, multiply both sides by −2-2 to isolate h+2h + 2 on one side:−6×(−2)=h+2-6 \times (-2) = h + 212=h+212 = h + 2
  4. Find value of h: Subtract 22 from both sides to find the value of hh.\newline12−2=h12 - 2 = h\newline10=h10 = h

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