Question

which statement about these equations is true?
equation a: ( y = 3x + 4 )
equation b: ( y = 3x + 2 )
a equation a has a greater rate of change.
b equation a has a greater initial value.
c equation b has a greater initial value.
d both equations have the same initial value.
which statement is true?

Explanation:

Step1: Identify slope (rate of change)

For linear equations in $y=mx+b$ form, $m$ is the rate of change.
Equation A: $m_A=3$; Equation B: $m_B=3$

Step2: Identify initial value (y-intercept)

In $y=mx+b$, $b$ is the initial value.
Equation A: $b_A=4$; Equation B: $b_B=2$

Step3: Compare values

Rates of change are equal. Initial value of A ($4$) > Initial value of B ($2$).

Answer:

B. Equation A has a greater initial value.