Find the equation of the line. Write the equation of the line in standard form.
With slope -1/2​; ​y-intercept 8

To find the equation of a line in standard form given the slope and y-intercept, we follow these steps:

### Step 1: Start with the slope-intercept form
The slope-intercept form of a line is:

\[
y = mx + b
\]

Where:
- \( m \) is the slope.
- \( b \) is the y-intercept.

Given:
- \( m = -\frac{1}{2} \)
- \( b = 8 \)

So, the equation is:

\[
y = -\frac{1}{2}x + 8
\]

### Step 2: Convert to standard form
The standard form of a line is:

\[
Ax + By = C
\]

To convert, we eliminate the fraction by multiplying through by 2:

\[
2y = -x + 16
\]

Next, rearrange to bring all terms involving \(x\) and \(y\) to one side:

\[
x + 2y = 16
\]

### Final Equation:
The equation of the line in standard form is:

\[
x + 2y = 16
\]

Would you like more details, or do you have any questions? 

Here are 5 related questions to expand your understanding:
1. How do you find the slope of a line if two points are given?
2. What is the difference between standard form and slope-intercept form?
3. How can you convert from standard form to slope-intercept form?
4. Can all linear equations be written in standard form?
5. What are the characteristics of horizontal and vertical lines in standard form?

**Tip**: When working with standard form, always aim to have integer coefficients for \(A\), \(B\), and \(C\).

Find the equation of the line. Write the equation of the line in standard form. With slope -1/2; y-intercept 8

Learn how to find the equation of a line with slope -1/2 and y-intercept 8. This step-by-step solution converts the equation from slope-intercept form (y = -1/2x + 8) to standard form (x + 2y = 16). Suitable for Grades 7-9 students studying linear equations.

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