Question

function a and function b are linear functions.
function a
function b
x\ty
-2\t0
-1\t1
6\t8
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 y-intercept of Function A

The graph of Function A crosses the y-axis at $(0,1)$, so its y-intercept is $1$.

Step2: Find equation of Function B

First calculate slope: $m=\frac{y_2-y_1}{x_2-x_1}=\frac{1-0}{-1-(-2)}=\frac{1}{1}=1$.
Use point-slope form $y-y_1=m(x-x_1)$ with $(-2,0)$:
$y-0=1(x-(-2))$
$y=x+2$

Step3: Identify y-intercept of Function B

From $y=x+2$, the y-intercept is $2$.

Step4: Compare the two y-intercepts

$1 < 2$, so Function A's y-intercept is smaller.

Answer:

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