Question

find the y-intercept of the line $y = -\frac{8}{5}x - 4$. write your answer as an integer or as a simplified proper or improper fra ordered pair.

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 y - intercept is the point where the line crosses the y - axis, and at this point, $x = 0$. So we can also find the y - intercept by setting $x = 0$ in the equation of the line and solving for $y$.

Step2: Substitute $x = 0$ into the equation

Given the line $y=-\frac{8}{5}x - 4$, when $x = 0$, we substitute $x$ with 0:
$y=-\frac{8}{5}(0)-4$

Step3: Simplify the expression

First, calculate $-\frac{8}{5}(0)=0$. Then, $y = 0 - 4=-4$. In ordered pair form, since $x = 0$ when the line crosses the y - axis, the y - intercept as an ordered pair is $(0,-4)$. If we just want the value of the y - intercept (the $y$ - value when $x = 0$), it is $-4$.

Answer:

$(0, - 4)$ (or just $-4$ if we consider the y - value of the y - intercept)