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 slope - undefined 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 passing through \((x_1,y_1)\), the \(x\) - coordinate \(x_1\) is constant for all points on the line. Here, \(x_1=-4\), so the equation of the vertical line is \(x=-4\). In standard form \(Ax + By=C\), we can write it as \(x+0y=-4\), where \(A = 1\), \(B = 0\), and \(C=-4\) (and 1, 0, - 4 are relatively prime integers).

Answer:

\(x=-4\) (or in standard form \(x + 0y=-4\))