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Put the following equation of a line into slope-intercept form, simplifying all fractions. 3x-2y=-14 Answer:

Put the following equation of a line into slope-intercept form, simplifying all fractions.\newline3x−2y=−14 3 x-2 y=-14 \newlineAnswer:

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Full solution

Q. Put the following equation of a line into slope-intercept form, simplifying all fractions.\newline3x−2y=−14 3 x-2 y=-14 \newlineAnswer:
  1. Move x term: Isolate the term with y on one side of the equation.\newlineTo do this, we will move the term with x to the other side by subtracting 3x3x from both sides of the equation.\newline3x−2y−3x=−14−3x3x - 2y - 3x = -14 - 3x\newlineThis simplifies to:\newline−2y=−3x−14-2y = -3x - 14
  2. Divide by coefficient: Divide every term by the coefficient of yy to solve for yy. The coefficient of yy is −2-2, so we divide each term by −2-2 to isolate yy. (−2y)/(−2)=(−3x)/(−2)−14/(−2)(-2y) / (-2) = (-3x) / (-2) - 14 / (-2) This simplifies to: y=(3/2)x+7y = (3/2)x + 7
  3. Check slope-intercept form: Check that the equation is now in slope-intercept form. The slope-intercept form is y=mx+by = mx + b, where mm is the slope and bb is the y-intercept. Our equation y=32x+7y = \frac{3}{2}x + 7 is in this form, with a slope of 32\frac{3}{2} and a y-intercept of 77.

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