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What is the equation of the line that passes through the point (-2,-4) and has a slope of 1 ? Answer:

What is the equation of the line that passes through the point (−2,−4) (-2,-4) and has a slope of 11 ?\newlineAnswer:

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Q. What is the equation of the line that passes through the point (−2,−4) (-2,-4) and has a slope of 11 ?\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: 11\newlinePoint (x1,y1)(x_1, y_1): (−2,−4)(-2, -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 slope and coordinates: Substitute the slope and the coordinates of the point into the point-slope form equation.\newlineUsing the point (−2,−4)(-2, -4) and the slope 11, we get:\newliney−(−4)=1(x−(−2))y - (-4) = 1(x - (-2))\newlineSimplify the equation by removing the parentheses and combining like terms.\newliney+4=1(x+2)y + 4 = 1(x + 2)
  3. Distribute slope: Distribute the slope 11 on the right side of the equation.y+4=1×x+1×2y + 4 = 1 \times x + 1 \times 2This simplifies to:y+4=x+2y + 4 = x + 2
  4. Isolate y: 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=x+2−4y = x + 2 - 4\newlineCombine like terms:\newliney=x−2y = x - 2

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