Question

1. identify whether the lines are parallel, perpendicular, or neither.

2y = 5x + 14
-5x + 2y = 7
options: neither, perpendicular, parallel

Explanation:

Step1: Convert first equation to slope - intercept form

The first equation is \(2y = 5x+14\). Divide each term by 2: \(y=\frac{5}{2}x + 7\). The slope \(m_1\) of this line is \(\frac{5}{2}\).

Step2: Convert second equation to slope - intercept form

The second equation is \(- 5x+2y = 7\). Add \(5x\) to both sides: \(2y=5x + 7\). Divide each term by 2: \(y=\frac{5}{2}x+\frac{7}{2}\). The slope \(m_2\) of this line is \(\frac{5}{2}\).

Step3: Compare the slopes

For two lines to be parallel, their slopes must be equal (\(m_1=m_2\)). Here, \(m_1 = \frac{5}{2}\) and \(m_2=\frac{5}{2}\), so \(m_1=m_2\).

Answer:

Parallel