Find the slope and the $$ y $$-intercept of the line. $$ 4 x-2 y=-3 $$ Write your answers in simplest form.

Question

UpStudy AI · Accepted Answer

To find the slope and the $$ y $$-intercept of the line given by the equation

$$
4x - 2y = -3,
$$

we can rearrange this equation into the slope-intercept form, which is

$$
y = mx + b,
$$

where $$ m $$ is the slope and $$ b $$ is the $$ y $$-intercept.

Starting with the original equation:

$$
4x - 2y = -3,
$$

we can isolate $$ y $$ by following these steps:

1. Subtract $$ 4x $$ from both sides:

$$
-2y = -4x - 3.
$$

2. Divide every term by $$-2$$ to solve for $$ y $$:

$$
y = \frac{-4x}{-2} + \frac{-3}{-2}.
$$

This simplifies to:

$$
y = 2x + \frac{3}{2}.
$$

Now, we can identify the slope and the $$ y $$-intercept from the equation $$ y = 2x + \frac{3}{2} $$:

- The slope $$ m $$ is $$ 2 $$.
- The $$ y $$-intercept $$ b $$ is $$ \frac{3}{2} $$.

Thus, the slope and the $$ y $$-intercept of the line are:

$$
\text{slope} = 2, \quad \text{y-intercept} = \frac{3}{2}.
$$
The slope is 2 and the $$ y $$-intercept is $$ \frac{3}{2} $$.

Find the slope and the \( y \)-intercept of the line. \[ 4 x-2 y=-3 \] Write your answers in simplest form.