If (5y=px+25) has (y)-intercept (5), which statement is correct?

Correct answer: For every (p), the (y)-intercept will be (5)

The direct answer is option D: for every value of \(p\), the y-intercept is 5. The y-intercept is the value of \(y\) when \(x=0\). Starting with \(5y=px+25\), divide every term by 5: \(y=\frac{p}{5}x+5\). This is the form \(y=mx+c\), where \(m\) is the slope and \(c\) is the y-intercept. Thus the slope is \(\frac p5\), which changes with \(p\), but the constant term remains 5. Option A, only \(p=5\), is wrong because no special value of \(p\) is needed. Option B, only \(p=25\), is similarly unsupported. Option C, no \(p\), is wrong because every allowed value of \(p\) leaves the constant term unchanged. Option D is correct because putting \(x=0\) directly gives \(5y=25\), hence \(y=5\), regardless of \(p\). Exam cue: in a line written as \(y=mx+c\), read the y-intercept from the constant term.