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A line has a slope of 33 and includes the points (−8,3)(-8,3) and (−7,v)(-7,v). What is the value of vv?\newlinev = ____

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Full solution

Q. A line has a slope of 33 and includes the points (−8,3)(-8,3) and (−7,v)(-7,v). What is the value of vv?\newlinev = ____
  1. Use Slope Formula: To find the value of vv, we can use the slope formula, which is (change in y)/(change in x)=slope(\text{change in } y) / (\text{change in } x) = \text{slope}. Since we know the slope of the line is 33, and we have the coordinates of two points on the line, (−8,3)(-8,3) and (−7,v)(-7,v), we can plug these values into the slope formula to find vv.
  2. Denote Given Points: First, let's denote the given points as (x1,y1)=(−8,3)(x_1, y_1) = (-8, 3) and (x2,y2)=(−7,v)(x_2, y_2) = (-7, v). The slope formula is (y2−y1)/(x2−x1)=slope(y_2 - y_1) / (x_2 - x_1) = \text{slope}. We can substitute the known values into this formula: (v−3)/(−7−(−8))=3(v - 3) / (-7 - (-8)) = 3.
  3. Substitute Values: Now, let's simplify the denominator of the fraction: (−7−(−8))=(−7+8)=1(-7 - (-8)) = (-7 + 8) = 1. So, the equation becomes (v−3)/1=3(v - 3) / 1 = 3.
  4. Simplify Denominator: Since dividing by 11 does not change the value, we can simplify the equation further to v−3=3v - 3 = 3.
  5. Simplify Equation: To find the value of vv, we add 33 to both sides of the equation: v−3+3=3+3v - 3 + 3 = 3 + 3, which simplifies to v=6v = 6.

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