https://file.aiquickdraw.com/mathbot/file/1725586414627c6wkfr9y.jpg

Let's break down the problem in the image step by step.

### Problem 1 (a): 
We are asked to find the equation of a line that passes through two points: (-4, -3) and (1, -6). The equation needs to be expressed in standard form.

The standard form of a line is:
\[
Ax + By = C
\]
where \(A\), \(B\), and \(C\) are integers.

To find the equation of the line, we will:
1. First, calculate the slope (\(m\)) using the two points.
2. Use the point-slope form of a line, \(y - y_1 = m(x - x_1)\), to find the equation.
3. Convert the equation to standard form.

#### Step 1: Calculate the slope

The formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Substituting the given points:
\[
m = \frac{-6 - (-3)}{1 - (-4)} = \frac{-6 + 3}{1 + 4} = \frac{-3}{5}
\]
So, the slope \(m = -\frac{3}{5}\).

#### Step 2: Point-slope form

Using the point \((1, -6)\) and the slope we found, the point-slope form of the line is:
\[
y - (-6) = -\frac{3}{5}(x - 1)
\]
Simplifying:
\[
y + 6 = -\frac{3}{5}(x - 1)
\]

#### Step 3: Convert to standard form

To convert to standard form, first distribute the slope:
\[
y + 6 = -\frac{3}{5}x + \frac{3}{5}
\]
Multiply the entire equation by 5 to eliminate the fraction:
\[
5(y + 6) = -3(x - 1)
\]
\[
5y + 30 = -3x + 3
\]

Rearrange the equation to standard form \(Ax + By = C\):
\[
3x + 5y = -27
\]

Thus, the equation of the line in standard form is:
\[
3x + 5y = -27
\]

---

### Problem 1 (b):
We are asked to find the \(x\)- and \(y\)-intercepts using the equation from part (a).

1. **To find the \(x\)-intercept**: Set \(y = 0\) in the equation and solve for \(x\):
\[
3x + 5(0) = -27 \quad \Rightarrow \quad 3x = -27 \quad \Rightarrow \quad x = -9
\]
So, the \(x\)-intercept is \((-9, 0)\).

2. **To find the \(y\)-intercept**: Set \(x = 0\) in the equation and solve for \(y\):
\[
3(0) + 5y = -27 \quad \Rightarrow \quad 5y = -27 \quad \Rightarrow \quad y = -\frac{27}{5}
\]
So, the \(y\)-intercept is \(\left(0, -\frac{27}{5}\right)\).

---

Would you like more details or have any questions about the steps?

Here are 5 related questions:
1. How do you find the slope of a line given two points?
2. What is the difference between slope-intercept form and standard form of a line?
3. How do you convert from point-slope form to standard form?
4. How do you find intercepts from the standard form of a line?
5. How can you check if a given point lies on the line described by an equation?

**Tip**: Always double-check your work by substituting the points back into the final equation to confirm that they satisfy it!

Find the equation of the line that passes through (-4, -3) and (1, -6) and express it in standard form. Then, find the x- and y-intercepts.

Learn how to find the equation of a line that passes through the points (-4, -3) and (1, -6) and express it in standard form. This problem involves calculating the slope, using point-slope form, and converting to standard form. Suitable for Grades 9-10.

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