Put the following equation of a line into slope-intercept form, simplifying all fractions.
8, y, minus, 2, x, equals, minus, 40
8y−2x=
−40

To rewrite the given equation \( 8y - 2x = -40 \) in slope-intercept form (which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept), follow these steps:

### Step 1: Isolate the term with \( y \)
Add \( 2x \) to both sides to move the \( x \)-term to the right side:
\[
8y = 2x - 40
\]

### Step 2: Solve for \( y \)
Divide everything by 8 to get \( y \) alone:
\[
y = \frac{2x}{8} - \frac{40}{8}
\]

### Step 3: Simplify the fractions
Simplify the fractions:
\[
y = \frac{1}{4}x - 5
\]

Thus, the equation in slope-intercept form is:
\[
y = \frac{1}{4}x - 5
\]

### Conclusion:
The slope is \( \frac{1}{4} \), and the y-intercept is \( -5 \).

Would you like further details or have any questions?

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Here are some related questions:
1. How do you find the slope from an equation in standard form?
2. What is the importance of the y-intercept in the slope-intercept form?
3. How do you graph a line using the slope-intercept form?
4. What does a positive slope indicate about the line's direction?
5. How would the equation change if the slope were negative?

**Tip:** Always check that your fractions are fully simplified when rewriting equations.

Put the following equation of a line into slope-intercept form, simplifying all fractions: 8y - 2x = -40

Learn how to convert the linear equation 8y - 2x = -40 into slope-intercept form (y = mx + b) with a step-by-step explanation. This problem covers key algebraic concepts like isolating variables and simplifying fractions. Suitable for students in Grades 7-10.

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