Find the slope and the 

*y*

-intercept of the line.

=+−12*x*4*y*−8

Write your answers in simplest form.

To find the slope and the \( y \)-intercept of the line given by the equation \( -12x + 4y = -8 \), we'll first rewrite the equation in slope-intercept form, \( y = mx + b \), where \( m \) is the slope and \( b \) is the \( y \)-intercept.

### Step 1: Solve for \( y \)
Start with the given equation:

\[
-12x + 4y = -8
\]

Add \( 12x \) to both sides:

\[
4y = 12x - 8
\]

Now, divide every term by 4 to isolate \( y \):

\[
y = \frac{12x}{4} - \frac{8}{4}
\]

Simplify:

\[
y = 3x - 2
\]

### Step 2: Identify the slope and \( y \)-intercept
In the equation \( y = 3x - 2 \):

- The slope \( m \) is \( 3 \).
- The \( y \)-intercept \( b \) is \( -2 \).

So, the slope of the line is \( 3 \), and the \( y \)-intercept is \( -2 \).

Would you like further details on this process, or do you have any other questions?

Here are 8 related questions for further exploration:

1. How do you find the \( y \)-intercept if given only two points on the line?
2. What is the equation of a line parallel to \( y = 3x - 2 \)?
3. How do you convert an equation from standard form to slope-intercept form?
4. What does a positive slope indicate about the direction of the line?
5. How do you find the \( x \)-intercept of the line given by \( y = 3x - 2 \)?
6. What is the slope of a line perpendicular to \( y = 3x - 2 \)?
7. How would the equation change if the line were to shift upwards by 4 units?
8. How can you determine the slope and intercepts if the equation is given in point-slope form?

**Tip:** Converting an equation to slope-intercept form is often the quickest way to identify the slope and \( y \)-intercept directly.

Learn how to find the slope and y-intercept of the line given by the equation -12x + 4y = -8 with a step-by-step solution. This problem covers linear equations and the slope-intercept form. Suitable for students in Grades 7-9.

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