Which equation is equivalent to 5x - 4y = 24?
Understand the Problem
The question is asking to identify which of the provided equations is equivalent to the equation 5x - 4y = 24. To solve this, we need to manipulate the original equation to find equivalent forms.
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
- Rearranging the original equation
Start with the given equation: $$ 5x - 4y = 24 $$
We want to isolate (y) on one side of the equation.
- Isolate the term with (y)
Subtract (5x) from both sides: $$ -4y = -5x + 24 $$
- Solve for (y)
Now, divide each term by (-4) to solve for (y): $$ y = \frac{5}{4}x - 6 $$
- Select the equivalent equation
Now we can compare our result ( y = \frac{5}{4}x - 6 ) with the provided options:
- The second option: ( y = -\frac{5}{4}x + 6 ) is not equivalent.
- The third option: ( y = \frac{5}{4}x - 6 ) matches our result.
- The fourth option: ( y = 5x - 6 ) is not equivalent.
- The first option: ( 1y = 24 ) is also not equivalent.
Therefore, the correct answer is the third option.
The equation equivalent to (5x - 4y = 24) is $$ y = \frac{5}{4}x - 6 $$.
More Information
The equivalent equation represents the same line in the coordinate plane. In this case, it shows the relationship between (x) and (y) in slope-intercept form, where the slope is (\frac{5}{4}) and the y-intercept is (-6).
Tips
- A common mistake might be incorrectly distributing the negative sign when isolating (y). It's critical to carefully follow each step and verify calculations to avoid errors.