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Put the following equation of a line into slope-intercept form, simplifying all fractions. 3x+3y=21 Answer:

Put the following equation of a line into slope-intercept form, simplifying all fractions.\newline3x+3y=21 3 x+3 y=21 \newlineAnswer:

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Full solution

Q. Put the following equation of a line into slope-intercept form, simplifying all fractions.\newline3x+3y=21 3 x+3 y=21 \newlineAnswer:
  1. Isolate y-term: 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 isolating the yy-term on one side of the equation.\newline3x+3y=213x + 3y = 21\newlineSubtract 3x3x from both sides to get the yy-term by itself.\newline3y=−3x+213y = -3x + 21
  2. Divide by coefficient: Now, we need to divide every term by the coefficient of yy, which is 33, to solve for yy.3y3=−3x3+213\frac{3y}{3} = \frac{-3x}{3} + \frac{21}{3}This simplifies to:y=−x+7y = -x + 7
  3. Convert to slope-intercept form: We have now put the equation into slope-intercept form. The slope mm is −1-1, and the y-intercept bb is 77.

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