Question

Compare the x-intercepts for the two linear functions represented below.

A.
The x-intercept of function A is greater than the x-intercept of function B.
B.
The x-intercept of function A is less than the x-intercept of function B.
C.
The x-intercept of function A is same as the x-intercept of function B.

Answer 1

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

Step-by-step explanation:

Function A is an equation in the form y = mx + b, where m is the slope, or rate of change, and b represents the y-intercept.

For function A, b = 3, so the y-intercept is (0,3).

For function B, the y-intercept of the graph is the point at which the line crosses the y-axis, (0,2).

Since 3 is greater than 2, the y-intercept of function A is greater than the y-intercept of function B.

Answer 2

B. The x-intercept of function A is less than that of function B.

Step-by-step explanation:

Both functions have y-intercepts of -1. Function A has a slope of 2, while function B has a slope of 1. Since Function A has a steeper slope, its x-intercept will be closer to x=0 than that of Function B.

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The x-intercept of Function B is given as (1, 0). The x-intercept of Function A can be found by solving for x when y=0:

... 0 = 2x -1

... 0 = x - 1/2 . . . . divide by 2

... 1/2 = x . . . . . . . the x-intercept is (1/2, 0), so is less than (1, 0)