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Write and equation for a line passing through this point, and with this slope {:[(2","6)],[m=3]:} {:[y=3x],[y=3x+2],[y=x+3],[y=1//2x+3]:}

Write and equation for a line passing through this point, and with this slope\newline(2,6)m=3 \begin{array}{l} (2,6) \\ m=3 \end{array} \newliney=3xy=3x+2y=x+3y=12x+3 \begin{array}{l} y=3 x \\ y=3 x+2 \\ y=x+3 \\ y=\frac{1}{2} x+3 \end{array}

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Full solution

Q. Write and equation for a line passing through this point, and with this slope\newline(2,6)m=3 \begin{array}{l} (2,6) \\ m=3 \end{array} \newliney=3xy=3x+2y=x+3y=12x+3 \begin{array}{l} y=3 x \\ y=3 x+2 \\ y=x+3 \\ y=\frac{1}{2} x+3 \end{array}
  1. Start with Point-Slope Form: Use the point-slope form of the equation of a line to start the problem.\newlineThe point-slope form is given by (y−y1)=m(x−x1)(y - y_1) = m(x - x_1), where mm is the slope and (x1,y1)(x_1, y_1) is the point the line passes through.\newlineGiven point: (2,6)(2, 6)\newlineGiven slope: m=3m = 3
  2. Substitute Point and Slope: Substitute the given point and slope into the point-slope form equation.\newline(y−6)=3(x−2)(y - 6) = 3(x - 2)
  3. Distribute Slope: Distribute the slope on the right side of the equation.\newline(y−6)=3x−6(y - 6) = 3x - 6
  4. Add 66 to Solve for y: Add 66 to both sides of the equation to solve for yy.\newliney=3x−6+6y = 3x - 6 + 6\newliney=3xy = 3x
  5. Check Answer Choices: Check the answer choices to see which one matches the derived equation.\newlineThe correct equation is y=3xy = 3x, which is one of the choices provided.

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