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What is the equation of the line that passes through the point (1,3) and has a slope of -2 ? Answer:

What is the equation of the line that passes through the point (1,3) (1,3) and has a slope of −2-2 ?\newlineAnswer:

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Q. What is the equation of the line that passes through the point (1,3) (1,3) and has a slope of −2-2 ?\newlineAnswer:
  1. Identify slope and point: Identify the slope mm and the point (x1,y1)(x_1, y_1) through which the line passes.\newlineWe have:\newlineSlope mm: −2-2\newlinePoint (x1,y1)(x_1, y_1): (1,3)(1, 3)\newlineWe will use the point-slope form of the equation of a line, which is y−y1=m(x−x1)y - y_1 = m(x - x_1), to find the equation of the line.
  2. Substitute slope and point: Substitute the slope and the point into the point-slope form equation.\newlineUsing the point (1,3)(1, 3) and the slope −2-2, the equation becomes:\newliney−3=−2(x−1)y - 3 = -2(x - 1)
  3. Distribute slope: Distribute the slope −2-2 on the right side of the equation.\newliney−3=−2x+2y - 3 = -2x + 2
  4. Add to solve for y: Add 33 to both sides of the equation to solve for yy and put the equation in slope-intercept form (y=mx+by = mx + b).\newliney=−2x+2+3y = -2x + 2 + 3\newliney=−2x+5y = -2x + 5

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