$$ 1

Question

$$ 1<\quad $$ Use intercepts to graph the equation. $$ 3 x-5 y-15=0 $$

UpStudy AI · Accepted Answer

To graph the equation $$ 3x - 5y - 15 = 0 $$ using intercepts, we will find both the x-intercept and the y-intercept.

### Step 1: Find the x-intercept
The x-intercept occurs when $$ y = 0 $$. We can find it by substituting $$ y = 0 $$ into the equation:

$$
3x - 5(0) - 15 = 0
$$

This simplifies to:

$$
3x - 15 = 0
$$

Now, solving for $$ x $$:

$$
3x = 15 \
x = 5
$$

So, the x-intercept is $$ (5, 0) $$.

### Step 2: Find the y-intercept
The y-intercept occurs when $$ x = 0 $$. We can find it by substituting $$ x = 0 $$ into the equation:

$$
3(0) - 5y - 15 = 0
$$

This simplifies to:

$$
-5y - 15 = 0
$$

Now, solving for $$ y $$:

$$
-5y = 15 \
y = -3
$$

So, the y-intercept is $$ (0, -3) $$.

### Step 3: Plot the intercepts
Now that we have both intercepts, we can plot the points $$ (5, 0) $$ and $$ (0, -3) $$ on a coordinate plane.

### Step 4: Draw the line
Finally, we can draw a straight line through these two points to represent the equation $$ 3x - 5y - 15 = 0 $$.

### Summary of intercepts:
- x-intercept: $$ (5, 0) $$
- y-intercept: $$ (0, -3) $$

This completes the process of using intercepts to graph the equation.
To graph the equation $$ 3x - 5y - 15 = 0 $$, find the x-intercept at $$ (5, 0) $$ and the y-intercept at $$ (0, -3) $$. Plot these points and draw a line through them.

\( 1<\quad \) Use intercepts to graph the equation. \[ 3 x-5 y-15=0 \]

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