Find the $$ x $$ - and $$ y $$-intercepts of the graph of the equation. Do not graph the line. $$ -7 x-5 y=21 $$ $$ x $$-intercept $$ \quad(x, y)=(\square) $$ $$ y $$-intercept $$ \quad(x, y)=(\square) $$ SUBMIT ANSWER

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UpStudy AI · Accepted Answer

To find the $$ x $$- and $$ y $$-intercepts of the equation $$ -7x - 5y = 21 $$, we will follow these steps:

1. **Find the $$ x $$-intercept**: Set $$ y = 0 $$ and solve for $$ x $$.
2. **Find the $$ y $$-intercept**: Set $$ x = 0 $$ and solve for $$ y $$.

Let's perform these calculations step by step.

### Step 1: Find the $$ x $$-intercept
Set $$ y = 0 $$ in the equation:
$$
-7x - 5(0) = 21
$$
This simplifies to:
$$
-7x = 21
$$
Now, solve for $$ x $$:
$$
x = \frac{21}{-7}
$$

### Step 2: Find the $$ y $$-intercept
Set $$ x = 0 $$ in the equation:
$$
-7(0) - 5y = 21
$$
This simplifies to:
$$
-5y = 21
$$
Now, solve for $$ y $$:
$$
y = \frac{21}{-5}
$$

Now, I will calculate the values for $$ x $$ and $$ y $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{21}{\left(-7\right)}$$
- step1: Remove the parentheses:
  $$\frac{21}{-7}$$
- step2: Reduce the numbers:
  $$\frac{-3}{1}$$
- step3: Calculate:
  $$-3$$
Calculate or simplify the expression $$ 21/-5 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{21}{\left(-5\right)}$$
- step1: Remove the parentheses:
  $$\frac{21}{-5}$$
- step2: Rewrite the fraction:
  $$-\frac{21}{5}$$
The calculations yield the following results:

1. **$$ x $$-intercept**: 
   $$
(x, y) = (-3, 0)
   $$

2. **$$ y $$-intercept**: 
   $$
(x, y) = \left(0, -\frac{21}{5}\right) \quad \text{or} \quad (0, -4.2)
   $$

Thus, the intercepts are:
- $$ x $$-intercept: $$ ( -3, 0 ) $$
- $$ y $$-intercept: $$ \left( 0, -\frac{21}{5} \right) $$ or $$ (0, -4.2) $$
$$ x $$-intercept: $$ (-3, 0) $$ $$ y $$-intercept: $$ \left(0, -\frac{21}{5}\right) $$ or $$ (0, -4.2) $$

Find the - and -intercepts of the graph of the equation. Do not graph the line.

-intercept
-intercept
SUBMIT ANSWER

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Solution

Step 1: Find the -intercept

Step 2: Find the -intercept

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Find the - and -intercepts of the graph of the equation. Do not graph the line. -intercept -intercept SUBMIT ANSWER