Question

which equation has a negative y-intercept?
y= -3x - 5
y= 3x + 5
y= -3x + 5

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the $y$-intercept. To find the $y$-intercept, we can set $x = 0$. When $x = 0$, $y=b$. So we need to check the value of $b$ (the constant term) in each equation.

Step2: Analyze $y=-3x - 5$

For the equation $y=-3x - 5$, comparing with $y = mx + b$, we have $m=-3$ and $b = - 5$. Since $b=-5<0$, the $y$-intercept is negative.

Step3: Analyze $y = 3x+5$

For the equation $y = 3x + 5$, comparing with $y=mx + b$, we have $m = 3$ and $b=5$. Since $b = 5>0$, the $y$-intercept is positive.

Step4: Analyze $y=-3x + 5$

For the equation $y=-3x + 5$, comparing with $y=mx + b$, we have $m=-3$ and $b = 5$. Since $b=5>0$, the $y$-intercept is positive.

Answer:

$y=-3x - 5$