Question

Function A and Function B are linear functions.

Function A is y= 1/3x - 2

Function B is x. y
-10. -5
-8. -4
6. 3

Which statement is true?
1. The y intercept of Function A is greater than the y-intercept of function B

2. The y intercept of Function A is less than the y-intercept of function B

Answer 1

The y-intercept of Function A is -2, while the y-intercept of Function B is determined to be 0 after analyzing given points. Therefore, Function A's y-intercept is less than that of Function B.

Step-by-step explanation:

Comparing the y-intercepts of Function A and Function B involves examining the equation of Function A and the given points of Function B. Function A is y = 1/3x - 2, which means its y-intercept is -2, because that is where the function crosses the y-axis (when x=0). Looking at Function B, we observe that it passes through the points (-10, -5), (-8, -4), and (6, 3). We can determine the y-intercept of Function B by observing its pattern or calculating its slope using two points, e.g., (-10, -5) and (-8, -4). The slope m is (Þly/Þlt) = (y2 - y1) / (x2 - x1) = (-4 - (-5)) / (-8 - (-10)) = 1/2. Now we write the slope-intercept form of a linear equation as y = mx + b and use a point to solve for b.

Let's use the point (-10, -5): -5 = (1/2)(-10) + b, which simplifies to -5 = -5 + b, resulting in b = 0. Therefore, the y-intercept of Function B is 0, which is greater than the y-intercept of Function A.

Thus, the correct statement is: "The y-intercept of Function A is less than the y intercept of Function B."