Rewrite the following equation in slope-intercept form.




18*x* + 8*y* = 5


To rewrite the equation \( 18x + 8y = 5 \) in slope-intercept form (\( y = mx + b \)), follow these steps:

### Step 1: Isolate the \( y \) term
Start by moving the \( 18x \) term to the right side of the equation:

\[
8y = -18x + 5
\]

### Step 2: Solve for \( y \)
Next, divide every term by 8 to isolate \( y \):

\[
y = -\frac{18}{8}x + \frac{5}{8}
\]

### Step 3: Simplify the fractions
Simplify the fraction \(\frac{18}{8}\) to \(\frac{9}{4}\):

\[
y = -\frac{9}{4}x + \frac{5}{8}
\]

So, the equation in slope-intercept form is:

\[
y = -\frac{9}{4}x + \frac{5}{8}
\]

This form clearly shows the slope \( m = -\frac{9}{4} \) and the y-intercept \( b = \frac{5}{8} \).

Would you like to explore how this equation behaves on a graph, or do you have any other questions related to it?

Here are five related questions:
1. How would you find the x-intercept of this equation?
2. What is the significance of the slope in this equation?
3. Can you convert this slope-intercept form back into standard form?
4. How would this line compare to another line with a different slope?
5. What happens to the graph of the line if the slope is changed?

**Tip:** Understanding the slope-intercept form is useful for quickly determining the direction and steepness of a line on a graph.

Learn how to rewrite the equation 18x + 8y = 5 in slope-intercept form y = mx + b with a detailed step-by-step solution. This problem covers linear equations and the conversion to slope-intercept form. Suitable for high school students in Grades 9-12.

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