Question

write an equation (a) in standard form and (b) in slope - intercept form for the line described. through (5,2), parallel to y = - 9

Explanation:

Step 1: Analyze the given line

The line \( y = -9 \) is a horizontal line (since it has the form \( y = k \) where \( k \) is a constant). The slope of a horizontal line is \( 0 \).

Step 2: Determine the slope of the parallel line

Parallel lines have the same slope. So, the line we want to find also has a slope of \( 0 \).

Step 3: Find the equation in slope - intercept form (\( y=mx + b \))

The slope - intercept form of a line is \( y=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. We know that \( m = 0 \) and the line passes through the point \( (5,2) \). Substitute \( x = 5 \), \( y = 2 \) and \( m=0 \) into \( y=mx + b \):
\( 2=0\times5 + b \)
\( 2 = b \)
So, the slope - intercept form of the line is \( y=0x + 2 \), which simplifies to \( y = 2 \).

Step 4: Find the equation in standard form (\( Ax+By = C \), where \( A\), \( B \), and \( C \) are integers and \( A\geq0 \))

Starting from \( y = 2 \), we can rewrite it as \( 0x+1y=2 \).

Answer:

(a) Standard form: \( 0x + y=2 \) (or simply \( y = 2 \) can be written as \( 0x + 1y=2 \))
(b) Slope - intercept form: \( y=2 \)