Find the slope and the $$ y $$-intercept of the line. $$ 4 x-3 y=-15 $$ 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

$$
4x - 3y = -15,
$$

we will first rewrite the equation in the slope-intercept form, which is

$$
y = mx + b,
$$

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

### Step 1: Solve for $$ y $$

Starting with the original equation:

$$
4x - 3y = -15,
$$

we will isolate $$ y $$ on one side of the equation.

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

$$
-3y = -4x - 15.
$$

2. Now, divide every term by $$-3$$ to solve for $$ y $$:

$$
y = \frac{4}{3}x + 5.
$$

### Step 2: Identify the slope and $$ y $$-intercept

From the equation $$ y = \frac{4}{3}x + 5 $$:

- The slope $$ m $$ is $$ \frac{4}{3} $$.
- The $$ y $$-intercept $$ b $$ is $$ 5 $$.

### Final Answer

- Slope: $$ \frac{4}{3} $$
- $$ y $$-intercept: $$ 5 $$
The slope is $$ \frac{4}{3} $$ and the $$ y $$-intercept is $$ 5 $$.

Find the slope and the \( y \)-intercept of the line. \[ 4 x-3 y=-15 \] Write your answers in simplest form.