Which equation is equivalent to 5x - 4y = 24?
Understand the Problem
The question is asking for a different form of the equation 5x - 4y = 24, specifically which choice presented is equivalent to this equation. This involves rearranging the equation and isolating y.
Answer
The equivalent equation is \( y = \frac{5}{4}x - 6 \).
Answer for screen readers
The equation equivalent to (5x - 4y = 24) is
$$ y = \frac{5}{4}x - 6 $$
Steps to Solve
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Start with the original equation
Begin with the equation we need to rearrange:
$$ 5x - 4y = 24 $$
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Isolate the term with y
Move the term (5x) to the other side of the equation:
$$ -4y = -5x + 24 $$
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Divide by -4 to solve for y
To isolate (y), divide each term by -4:
$$ y = \frac{5}{4}x - 6 $$
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Identifying the equivalent equation
Now we can compare this with the given options to find the equivalent equation.
The equation equivalent to (5x - 4y = 24) is
$$ y = \frac{5}{4}x - 6 $$
More Information
This form represents the linear equation in slope-intercept form (y = mx + b), where (m) is the slope and (b) is the y-intercept. Here, the slope is (\frac{5}{4}) and the y-intercept is -6.
Tips
- Failing to distribute the negative sign when isolating y.
- Confusing the operations when dividing or multiplying both sides of the equation. Always keep the equation balanced.
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