Question

multiple choice 4 points
graph ( y = x - 1 ) and ( y = 3x + 1 ). how many times do the two graphs intersect?
graph omitted
( \bigcirc ) 3
( \bigcirc ) 2
( \bigcirc ) 0
( \bigcirc ) 1

Explanation:

Step1: Set equations equal

$x - 1 = 3x + 1$

Step2: Solve for x

$-1 - 1 = 3x - x$
$-2 = 2x$
$x = -1$

Step3: Find y-value

$y = (-1) - 1 = -2$

Step4: Count intersection points

The system has one unique solution $(-1, -2)$, so the lines intersect once.

Answer:

1. 1