Question

identifying slope and y-intercept of a line
identify the slope and y-intercept of each linear functions equation
$-x + 3 = y$
$y = 1 - 3x$
$x - 3 = y$
$y = 3x - 1$
slope = 3, y-intercept at -1
slope = 1, y-intercept at -3
slope = -3, y-intercept at 1
slope = -1, y-intercept at 3

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 (the point where $x=0$).

Step2: Rewrite first equation

Rewrite $-x + 3 = y$ as $y = -1x + 3$. Here, $m=-1$, $b=3$.

Step3: Rewrite second equation

Rewrite $y = 1 - 3x$ as $y = -3x + 1$. Here, $m=-3$, $b=1$.

Step4: Rewrite third equation

Rewrite $x - 3 = y$ as $y = 1x - 3$. Here, $m=1$, $b=-3$.

Step5: Analyze fourth equation

For $y = 3x - 1$, it is already in slope-intercept form. Here, $m=3$, $b=-1$.

Answer:

$-x + 3 = y$ → slope = -1; y-intercept at 3
$y = 1 - 3x$ → slope = -3; y-intercept at 1
$x - 3 = y$ → slope = 1; y-intercept at -3
$y = 3x - 1$ → slope = 3; y-intercept at -1