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What is the equation of the line that passes through the point (-6,-4) and has a slope of 2? Answer:

What is the equation of the line that passes through the point (−6,−4) (-6,-4) and has a slope of 22?\newlineAnswer:

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Full solution

Q. What is the equation of the line that passes through the point (−6,−4) (-6,-4) and has a slope of 22?\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: 22\newlinePoint (x1,y1)(x_1, y_1): (−6,−4)(-6, -4)\newlineWe will use the point-slope form of the equation of a line to find the equation.\newlinePoint-slope form: y−y1=m(x−x1)y - y_1 = m(x - x_1)
  2. Substitute values into equation: Substitute the slope and the coordinates of the point into the point-slope form equation.\newlineUsing the point (−6,−4)(-6, -4) and the slope 22, we get:\newliney−(−4)=2(x−(−6))y - (-4) = 2(x - (-6))\newlineSimplify the equation by distributing the slope and removing parentheses.\newliney+4=2(x+6)y + 4 = 2(x + 6)
  3. Distribute slope: Distribute the slope on the right side of the equation.\newliney+4=2x+12y + 4 = 2x + 12
  4. Isolate yy in slope-intercept form: Isolate yy to get the equation in slope-intercept form (y=mx+by = mx + b).\newlineSubtract 44 from both sides of the equation to solve for yy.\newliney=2x+12−4y = 2x + 12 - 4\newliney=2x+8y = 2x + 8

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