Write an equation in slope-intercept form given 5x - 4y = -12.

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Understand the Problem

The question is asking to rearrange the equation 5x - 4y = -12 into slope-intercept form, which is y = mx + b. The user is required to express the equation correctly using specified formatting for fractions.

Answer

The equation in slope-intercept form is $$ y = \frac{5}{4}x + 3 $$
Answer for screen readers

The equation in slope-intercept form is

$$ y = \frac{5}{4}x + 3 $$

Steps to Solve

  1. Isolate the term with y

To rearrange the equation $5x - 4y = -12$, we first isolate the $y$ term by moving $5x$ to the right side of the equation.

[ -4y = -5x - 12 ]

  1. Divide by the coefficient of y

Next, we divide every term in the equation by $-4$ to solve for $y$.

[ y = \frac{-5x}{-4} + \frac{-12}{-4} ]

  1. Simplify the fractions

Now we simplify the fractions:

[ y = \frac{5}{4}x + 3 ]

The equation is now in slope-intercept form.

The equation in slope-intercept form is

$$ y = \frac{5}{4}x + 3 $$

More Information

In slope-intercept form $y = mx + b$, $m$ represents the slope and $b$ represents the y-intercept. Here, the slope is $\frac{5}{4}$, and the y-intercept is $3$.

Tips

  • Not isolating y correctly: Beginners may forget to move all terms to one side before isolating $y$.
  • Mistakes in dividing by negative numbers: Be careful with signs when dividing by a negative coefficient.

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