Question

write an equation (a) in standard form and (b) in slope-intercept form for the line described.

through \\((6,7)\\), parallel to \\(y = -6\\)

part 1 of 2

(a) the equation of the line in standard form is ______.
(type your answer in standard form.)

Explanation:

⚡ Using what you learned: parallel and perpendicular lines_equations

Step 1: Analyze the given line

The given line is:

$$ y = -6 $$

This is a horizontal line where the slope \( m = 0 \).

Any line parallel to a horizontal line must also be horizontal and have a slope of \( m = 0 \).

Step 2: Find the equation of the parallel line

The parallel line passes through the point \( (6, 7) \).

Since it is a horizontal line, its equation is determined solely by its \( y \)-coordinate:

$$ y = 7 $$

Step 3: Write in standard form

The standard form of a linear equation is \( Ax + By = C \).

For the horizontal line \( y = 7 \), we can write this as:

$$ 0x + y = 7 $$

Which simplifies to:

$$ y = 7 $$

Step 4: Write in slope-intercept form

The slope-intercept form is \( y = mx + b \).

Using \( m = 0 \) and \( b = 7 \):

$$ y = 0x + 7 $$

Which simplifies to:

$$ y = 7 $$

Answer:

(a) Standard form:

$$ y = 7 $$

(b) Slope-intercept form:

$$ y = 7 $$