Question

1. bret is examining a line with equation $y = 3x - 7$. he says that the $y$-intercept of the line is 7. is he correct? explain.

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the $y$-intercept.

Step2: Compare with given equation

The given equation is $y=3x - 7$. We can rewrite $-7$ as $+(-7)$, so the equation becomes $y = 3x+(-7)$.
Comparing with $y = mx + b$, we see that $m = 3$ (slope) and $b=-7$ ( $y$-intercept).

Step3: Evaluate Bret's statement

Bret said the $y$-intercept is $7$, but from the equation $y = 3x-7$, the $y$-intercept is $-7$. So Bret is incorrect.

Answer:

Bret is not correct. The slope - intercept form of a line is $y=mx + b$, where $b$ is the $y$-intercept. For the line $y = 3x-7$, we can rewrite it as $y=3x+(-7)$, so the $y$-intercept $b=-7$, not $7$.