equation of a line with y-intercept 8;  parallel to the line 5x + 6y + 2 = 0

To find the equation of a line that is parallel to the line \( 5x + 6y + 2 = 0 \) and has a \( y \)-intercept of 8, follow these steps:

### Step 1: Determine the slope of the given line
The general form of a line is \( Ax + By + C = 0 \). To find the slope, we rewrite the equation in slope-intercept form \( y = mx + b \), where \( m \) is the slope.

Given line: 
\[
5x + 6y + 2 = 0
\]
Solve for \( y \):
\[
6y = -5x - 2
\]
\[
y = -\frac{5}{6}x - \frac{1}{3}
\]

So, the slope of the given line is \( m = -\frac{5}{6} \).

### Step 2: Use the slope for the parallel line
Parallel lines have the same slope. So, the slope of the new line will also be \( m = -\frac{5}{6} \).

### Step 3: Use the y-intercept to form the equation
The equation of a line in slope-intercept form is \( y = mx + b \), where \( b \) is the \( y \)-intercept. Since the y-intercept is given as 8, the equation becomes:

\[
y = -\frac{5}{6}x + 8
\]

Thus, the equation of the line is:
\[
y = -\frac{5}{6}x + 8
\]

Alternatively, you can rewrite it in general form:
\[
5x + 6y - 48 = 0
\]

### Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:
1. How do you find the slope of a line given two points?
2. What is the general form of a linear equation?
3. How do you find the equation of a line perpendicular to a given line?
4. What is the significance of the y-intercept in a graph?
5. How do you convert from slope-intercept form to standard form?

**Tip:** Parallel lines have equal slopes, so identifying the slope is key when determining equations of parallel lines.

equation of a line with y-intercept 8; parallel to the line 5x + 6y + 2 = 0

Find the equation of a line that is parallel to 5x + 6y + 2 = 0 and has a y-intercept of 8. This detailed guide explains how to derive the equation using the slope-intercept form and discusses key concepts like parallel lines and slopes. Ideal for students in Grades 8-10.

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