Question

write an equation for the line that passes through (-4,6) and whose slope is undefined. give an answer in standard form.
write the equation in the standard form where all coefficients are expressed as relatively prime integers.

Explanation:

Step1: Recall undefined slope lines

A line with an undefined slope is a vertical line. The equation of a vertical line is of the form \( x = a \), where \( a \) is the x - coordinate of any point on the line.

Step2: Determine the value of \( a \)

The line passes through the point \( (-4,6) \). For a vertical line, the x - coordinate is constant. So, the x - coordinate of the point \( (-4,6) \) is \( - 4 \). So the equation of the line is \( x=-4 \).

Step3: Convert to standard form

The standard form of a linear equation is \( Ax + By = C \), where \( A \), \( B \), and \( C \) are integers, and \( A\geq0 \), and \( A \) and \( B \) are relatively prime.
Starting from \( x=-4 \), we can rewrite it as \( x+4 = 0 \). Here, \( A = 1 \), \( B = 0 \), and \( C=-4 \) (or we can also write it as \( x-(-4)=0 \) which is \( x + 4=0 \)). Since \( 1 \) and \( 0 \) are relatively prime (the greatest common divisor of \( 1 \) and \( 0 \) is \( 1 \)), this is in standard form.

Answer:

\( x+4 = 0 \)