function a and function b are linear functions. function a function b which statement is true? the y…

Explanation:

Step1: Find the y - intercept of Function A

The y - intercept of a linear function is the value of y when (x = 0). From the graph of Function A, when (x=0), (y = 3). So the y - intercept of Function A is (b_{A}=3).

Step2: Find the equation of Function B (to get its y - intercept)

The slope formula is (m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}). Let ((x_{1},y_{1})=(2,-3)) and ((x_{2},y_{2})=(3,-2)). Then (m=\frac{-2-\left(-3\right)}{3 - 2}=\frac{-2 + 3}{1}=1). Using the point - slope form (y-y_{1}=m(x - x_{1})), with (m = 1) and ((x_{1},y_{1})=(2,-3)), we have (y+3=1\times(x - 2)), which simplifies to (y=x-2 - 3=x - 5). The y - intercept of Function B is when (x = 0). Substituting (x = 0) into (y=x - 5), we get (y=-5). So (b_{B}=-5).

Step3: Compare the y - intercepts

Since (3>-5) (i.e., (b_{A}>b_{B}))

Answer:

The (y) - intercept of Function (A) is greater than the (y) - intercept of Function (B).