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A line that includes the points (−7,g)(-7,g) and (−4,−3)(-4,-3) has a slope of −3-3. What is the value of gg?\newlineg = ____

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Full solution

Q. A line that includes the points (−7,g)(-7,g) and (−4,−3)(-4,-3) has a slope of −3-3. What is the value of gg?\newlineg = ____
  1. Use Slope Formula: We are given two points: (−7,g)(-7, g) and (−4,−3)(-4, -3), and the slope of the line is −3-3. We will use the slope formula to find the value of gg.\newlineSlope mm = y2−y1x2−x1\frac{y_2 - y_1}{x_2 - x_1}\newline−3-3 = −3−g−4−(−7)\frac{-3 - g}{-4 - (-7)}
  2. Simplify Denominator: Simplify the denominator of the slope equation.\newline−3=−3−g−4+7-3 = \frac{-3 - g}{-4 + 7}\newline−3=−3−g3-3 = \frac{-3 - g}{3}
  3. Isolate Term with gg: Multiply both sides of the equation by 33 to isolate the term with gg.−3×3=−3−g3×3-3 \times 3 = \frac{-3 - g}{3} \times 3−9=−3−g-9 = -3 - g
  4. Add 33 to Both Sides: Add 33 to both sides of the equation to solve for gg.\newline−9+3=−3−g+3-9 + 3 = -3 - g + 3\newline−6=−g-6 = -g
  5. Multiply by −1-1: Multiply both sides by −1-1 to get the value of gg.−6×−1=−g×−1-6 \times -1 = -g \times -16=g6 = g

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