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What is the slope of the line represented by the equation 2x−5y=92x-5y=9?

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Full solution

Q. What is the slope of the line represented by the equation 2x−5y=92x-5y=9?
  1. Identify Equation Form: We are given the equation 2x−5y=92x - 5y = 9. Identify the form of the equation. The equation is in standard form Ax+By=CAx + By = C. We need to convert it to slope-intercept form y=mx+by = mx + b to find the slope.
  2. Convert to Slope-Intercept: Convert the standard form equation to slope-intercept form.\newlineStart by isolating yy on one side of the equation.\newlineSubtract 2x2x from both sides to get −5y=−2x+9-5y = -2x + 9.
  3. Solve for y: Divide each term by −5-5 to solve for y.\newliney=(−2x+9)/−5y = (-2x + 9) / -5\newliney=(2/5)x−9/5y = (2/5)x - 9/5\newlineNow the equation is in slope-intercept form, where mm is the slope.
  4. Identify the Slope: Identify the slope from the slope-intercept form.\newlineThe coefficient of xx in the equation y=25x−95y = \frac{2}{5}x - \frac{9}{5} is the slope.\newlineTherefore, the slope m=25m = \frac{2}{5}.

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