Question

function a and function b are linear functions. function a: x | y -4 | -17 -1 | -2 1 | 8 function b: y = x + 5 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.

Explanation:

Step1: Find slope of Function A

Use two points \((-4, -17)\) and \((-1, -2)\). Slope \(m = \frac{y_2 - y_1}{x_2 - x_1}=\frac{-2 - (-17)}{-1 - (-4)}=\frac{15}{3}=5\).

Step2: Find equation of Function A

Using point - slope form \(y - y_1 = m(x - x_1)\) with \((-1, -2)\) and \(m = 5\): \(y - (-2)=5(x - (-1))\), \(y + 2 = 5x+5\), \(y = 5x + 3\).

Step3: Find y - intercepts

For Function A (\(y = 5x+3\)), y - intercept is \(3\). For Function B (\(y=x + 5\)), y - intercept is \(5\).

Step4: Compare y - intercepts

Since \(3<5\), y - intercept of A is less than B.

Answer:

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