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To solve this, we need to find the equation of the line that passes through the point \((5, -7)\) and has a slope of \(-3\). 

The slope-intercept form of a line is given by:
\[
y = mx + b
\]
where \(m\) is the slope and \(b\) is the y-intercept.

### Step 1: Use the given slope and point
We substitute the slope \(m = -3\) and the point \((5, -7)\) into the equation to find \(b\).

\[
-7 = -3(5) + b
\]

Simplifying:
\[
-7 = -15 + b
\]

Add 15 to both sides:
\[
b = 8
\]

So, the equation in slope-intercept form is:
\[
y = -3x + 8
\]

### Step 2: Convert to standard form
The standard form of a line is:
\[
Ax + By = C
\]
We need to convert the slope-intercept form \(y = -3x + 8\) to standard form.

Start by moving the \(x\)-term to the left:
\[
3x + y = 8
\]

Thus, the standard form of the line is \(3x + y = 8\).

### Step 3: Compare with the options
From the choices given, the correct answer is **3x + y = 8**.

Would you like more details or have any questions? 

Here are some related questions you might find useful:
1. How do you convert a line from slope-intercept form to point-slope form?
2. What are the steps to convert an equation in standard form back to slope-intercept form?
3. Can you find the equation of a line given two points instead of the slope and one point?
4. What if the slope were positive? How would the equation change?
5. How can we graph a line given its equation in standard form?

**Tip:** Remember, when converting between forms of linear equations, it's important to maintain the correct structure for standard form: \(Ax + By = C\), where \(A\), \(B\), and \(C\) are integers, and \(A\) should be positive.

A line passes through the point (5, -7) and has a slope of -3. Which shows an equation for this line written in standard form?

Learn how to find the equation of a line that passes through the point (5, -7) and has a slope of -3. This question uses key concepts such as the slope-intercept form and converting to standard form. Suitable for Grades 8-10.

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