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

function a and function b are linear functions. which statement is true? the y - intercept of function a is greater than the y - intercept of function b. the y - intercept of function a is less than the y - intercept of function b.

function a and function b are linear functions. which statement is true? the y - intercept of function a is greater than the y - intercept of function b. the y - intercept of function a is less than the y - intercept of function b.

Answer

Explanation:

Step1: Find y - intercept of Function A

The y - intercept is the value of y when x = 0. From the graph of Function A, when x = 0, y = 3.

Step2: Find y - intercept of Function B

The equation of a line is y=mx + b, where b is the y - intercept. Using two points ((x_1,y_1)=(-1,-6)) and ((x_2,y_2)=(6,1)) to find the slope (m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{1-(-6)}{6 - (-1)}=\frac{7}{7}=1). Using the point - slope form (y - y_1=m(x - x_1)) with the point ((-1,-6)) and (m = 1), we have (y+6=1\times(x + 1)), which simplifies to (y=x - 5). So the y - intercept of Function B is - 5.

Step3: Compare y - intercepts

Since (3>-5), the y - intercept of Function A is greater than the y - intercept of Function B.

Answer:

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