Question

function p is a linear function with a y-intercept of 5. function q is defined by the equation $y = -2x + 3$.
which statement must be true about functions p and q?
○ both functions have the same slope.
○ both functions have a negative slope.
○ the functions will have the same input when $y = 5$
○ the functions will have different outputs when $x = 0$

Explanation:

Step1: Recall linear function form

A linear function is $y=mx+b$, where $m$=slope, $b$=y-intercept.

Step2: Analyze Function P

Function P has $b=5$, so its form is $y=m_p x + 5$, $m_p$ is unknown.

Step3: Analyze Function Q

Function Q: $y=-2x+3$, so $m_q=-2$, $b_q=3$.

Step4: Evaluate each option

• Option1: Same slope? $m_p$ is unknown, so false.
• Option2: Both negative slope? $m_p$ could be positive, so false.
• Option3: Same input at $y=5$?

For P: $5=m_p x +5 \implies x=0$.
For Q: $5=-2x+3 \implies x=-1$. Inputs differ, so false.

• Option4: Different outputs at $x=0$?

For P: $y=0*m_p +5=5$.
For Q: $y=-2*0+3=3$. $5
eq3$, so true.

Answer:

The functions will have different outputs when x = 0