Ask a New Question
Menu

Consider this system of equations. Which equation represents the first equation written in slope-intercept form?

5 x minus 2 y = 10. y = one-fourth x + 1.
y = five-halves x minus 5
y = five-halves x + 10
y = negative five-halves x + 10
y = negative 5 x minus 5

1 answer

To convert the equation \( 5x - 2y = 10 \) into slope-intercept form (which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept), follow these steps:

  1. Start with the original equation: \[ 5x - 2y = 10 \]

  2. Isolate the term involving \( y \) by subtracting \( 5x \) from both sides: \[ -2y = -5x + 10 \]

  3. Divide each term by \(-2\) to solve for \( y \): \[ y = \frac{5}{2}x - 5 \]

Now, we compare this result, \( y = \frac{5}{2}x - 5 \), to the given options:

  • \( y = \frac{1}{4}x + 1 \)
  • \( y = \frac{5}{2}x - 5 \)
  • \( y = \frac{5}{2}x + 10 \)
  • \( y = -\frac{5}{2}x + 10 \)
  • \( y = -5x - 5 \)

The correct equation representing the first equation in slope-intercept form is:

\[ y = \frac{5}{2}x - 5 \]