Question

function a (graph) and function b (table with x: -3,2,5 and y: -14,6,18). question: which statement is true? options: 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.

Explanation:

Step1: Find y-intercept of Function A

Function A is a line passing through the origin \((0,0)\), so its y-intercept \(b_A = 0\).

Step2: Find equation of Function B

The general form of a linear function is \(y = mx + b\). Using two points from Function B's table, e.g., \((-3, -14)\) and \((2, 6)\). First, calculate the slope \(m\):
\(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{6 - (-14)}{2 - (-3)}=\frac{20}{5}=4\)
Now, use point \((2, 6)\) to find \(b\):
\(6 = 4\times2 + b\)
\(6 = 8 + b\)
\(b = 6 - 8=-2\)
So, the y-intercept of Function B \(b_B=-2\).

Step3: Compare y-intercepts

Compare \(b_A = 0\) and \(b_B=-2\). Since \(0 > -2\), the y-intercept of Function A is greater than that of Function B.

Answer:

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