https://file.aiquickdraw.com/mathbot/file/1725580942981alwy8zk9.jpg

The problem from the image is asking for two tasks:

### Part (a)
- **Find the equation of the line** that passes through the points \((-1, -3)\) and \((1, -1)\). 
- **Express the answer in standard form**.

### Part (b)
- **Use the standard form of the equation** from part (a) to find the x- and y-intercepts.

Let's first solve part (a) by determining the equation of the line.

#### Step 1: Calculate the slope
The slope \( m \) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using the points \((-1, -3)\) and \((1, -1)\):
\[
m = \frac{-1 - (-3)}{1 - (-1)} = \frac{-1 + 3}{1 + 1} = \frac{2}{2} = 1
\]

#### Step 2: Use the point-slope form
The point-slope form of the equation of a line is:
\[
y - y_1 = m(x - x_1)
\]
Substitute \( m = 1 \) and the point \((-1, -3)\):

\[
y - (-3) = 1(x - (-1)) 
\]
\[
y + 3 = 1(x + 1)
\]
\[
y + 3 = x + 1
\]

#### Step 3: Rearrange to standard form
Standard form is \( Ax + By = C \), where \( A \), \( B \), and \( C \) are integers. Start by moving all terms to one side:

\[
y = x + 1 - 3
\]
\[
y = x - 2
\]

To convert to standard form, subtract \( x \) from both sides:
\[
x - y = 2
\]

This is the equation of the line in standard form.

### Part (b)
Now, let's find the **x-intercept** and **y-intercept** from the standard form equation \( x - y = 2 \).

- **To find the x-intercept**, set \( y = 0 \):
\[
x - 0 = 2 \implies x = 2
\]
Thus, the x-intercept is \( (2, 0) \).

- **To find the y-intercept**, set \( x = 0 \):
\[
0 - y = 2 \implies -y = 2 \implies y = -2
\]
Thus, the y-intercept is \( (0, -2) \).

### Summary
- The equation of the line in standard form is \( x - y = 2 \).
- The x-intercept is \( (2, 0) \).
- The y-intercept is \( (0, -2) \).

Would you like further details or explanations?

### 5 Related Questions:
1. How would you solve if one of the points involved a fraction?
2. How can the slope be used to identify parallel and perpendicular lines?
3. What is the significance of the standard form of a linear equation in graphing?
4. How would you find the equation of a line if only the slope and one point were given?
5. Can you generalize the relationship between the x- and y-intercepts for any linear equation?

### Tip:
When working with linear equations, always double-check your slope and intercepts, as small errors in calculation can affect the final result!

Find the equation of the line that passes through (-1, -3) and (1, -1). Express your answer in standard form. Then, use the standard form to find the x- and y-intercepts.

Learn how to find the equation of a line passing through the points (-1, -3) and (1, -1) with a step-by-step solution. This problem covers key algebraic concepts, including the slope formula, point-slope form, and standard form of a linear equation. Suitable for students in Grades 8-10.

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