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 $.

Steps to Solve

Start with the original equation

Begin with the equation we need to rearrange:

$$ 5x - 4y = 24 $$
Isolate the term with y

Move the term (5x) to the other side of the equation:

$$ -4y = -5x + 24 $$
Divide by -4 to solve for y

To isolate (y), divide each term by -4:

$$ y = \frac{5}{4}x - 6 $$
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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