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A line has a slope of −9-9 and includes the points (−6,3)(-6,3) and (−5,v)(-5,v). What is the value of vv?\newlinev = ____

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Full solution

Q. A line has a slope of −9-9 and includes the points (−6,3)(-6,3) and (−5,v)(-5,v). What is the value of vv?\newlinev = ____
  1. Set up equation using slope: To find the value of vv, we need to use the slope formula, which is (change in yy) / (change in xx). The slope of the line is given as −9-9, and we have the coordinates of two points on the line: (−6,3)(-6,3) and (−5,v)(-5,v). We can set up the equation using the slope and the coordinates of the points.
  2. Write equation for slope: The slope of the line is the same between any two points on the line. So, we can write the equation for the slope as follows:\newline−9=v−3−5−(−6)-9 = \frac{v - 3}{-5 - (-6)}
  3. Simplify denominator: Simplify the denominator of the fraction on the right side of the equation:\newline−9=v−3−5+6-9 = \frac{v - 3}{-5 + 6}
  4. Simplify equation: Now we have:\newline−9=v−31-9 = \frac{v - 3}{1}\newlineThis simplifies to:\newline−9=v−3-9 = v - 3
  5. Add 33 to both sides: To find the value of vv, we add 33 to both sides of the equation:\newline−9+3=v−3+3-9 + 3 = v - 3 + 3
  6. Find value of v: Simplify the equation to find the value of vv:−6=v-6 = v

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