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What is the slope of the line represented by the equation x-3y=10 ?

What is the slope of the line represented by the equation x−3y=10 x-3 y=10 ?

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Full solution

Q. What is the slope of the line represented by the equation x−3y=10 x-3 y=10 ?
  1. Identify Equation Type: We are given the equation x−3y=10x - 3y = 10. Identify the type of the equation. This is a linear equation in two variables, which can be written in slope-intercept form (y=mx+b)(y = mx + b) to find the slope.
  2. Rewrite in Slope-Intercept Form: Rewrite the equation in slope-intercept form.\newlineStart by isolating yy on one side of the equation.\newlineSubtract xx from both sides to get: −3y=−x+10-3y = -x + 10.
  3. Solve for y: Divide each term by −3-3 to solve for yy.y=−x+10−3y = \frac{-x + 10}{-3}.Simplify the equation to get: y=13x−103y = \frac{1}{3}x - \frac{10}{3}.
  4. Identify the Slope: Identify the slope from the slope-intercept form.\newlineThe coefficient of xx in the equation y=13x−103y = \frac{1}{3}x - \frac{10}{3} is the slope (mm).\newlineTherefore, the slope of the line is 13\frac{1}{3}.

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