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

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

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Full solution

Q. What is the slope of the line represented by the equation 2x−5y=9 2 x-5 y=9 ?
  1. Equation setup: To find the slope of the line represented by the equation 2x−5y=92x - 5y = 9, we need to solve for yy to get the equation into slope-intercept form, which is y=mx+by = mx + b, where mm is the slope.
  2. Isolating the y-term: First, we'll isolate the y-term on one side of the equation. We can do this by subtracting 2x2x from both sides of the equation.\newline2x−5y−2x=9−2x2x - 5y - 2x = 9 - 2x\newlineThis simplifies to:\newline−5y=−2x+9-5y = -2x + 9
  3. Dividing every term: Next, we divide every term by −5-5 to solve for yy.\newliney=−2x+9−5y = \frac{-2x + 9}{-5}
  4. Simplifying the equation: Now, we simplify the equation by dividing each term on the right side by -5＂).\(\newline\$y = \left(\frac{2}{5}\right)x - \frac{9}{5}\)
  5. Finding the slope: The equation is now in slope-intercept form, where the coefficient of \(x\) is the slope of the line.\(\newline\)So, the slope of the line is \(\frac{2}{5}\).

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