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Put the following equation of a line into slope-intercept form, simplifying all fractions. 5x-3y=12 Answer:

Put the following equation of a line into slope-intercept form, simplifying all fractions.\newline5x−3y=12 5 x-3 y=12 \newlineAnswer:

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Full solution

Q. Put the following equation of a line into slope-intercept form, simplifying all fractions.\newline5x−3y=12 5 x-3 y=12 \newlineAnswer:
  1. Move and Subtract 5x5x: To convert the equation into slope-intercept form, which is y=mx+by = mx + b, we need to solve for yy. Let's start by moving the term 5x5x to the right side of the equation by subtracting 5x5x from both sides.\newlineCalculation: 5x−3y−5x=12−5x5x - 3y - 5x = 12 - 5x\newlineThis simplifies to: −3y=−5x+12-3y = -5x + 12
  2. Isolate y: Now, we need to isolate y by dividing all terms by −3-3, the coefficient of y.\newlineCalculation: y=−5x+12−3y = \frac{-5x + 12}{-3}
  3. Simplify and Finalize: We can simplify the equation by dividing each term on the right side by −3-3.\newlineCalculation: y=−5−3x+12−3y = \frac{-5}{-3}x + \frac{12}{-3}\newlineThis simplifies to: y=53x−4y = \frac{5}{3}x - 4

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