Question

find an equation of the line described below. write the equation in slope-intercept form (solved for y), when possible. through (-6, -4), perpendicular to the y-axis what is the equation of the line?

Explanation:

Step1: Determine the slope of the line

A line perpendicular to the \( y \)-axis is a horizontal line. The slope of a horizontal line is \( 0 \) because the change in \( y \) (rise) is \( 0 \) for any change in \( x \) (run), and slope \( m=\frac{\text{rise}}{\text{run}}=\frac{0}{\text{run}} = 0 \) (where \(\text{run}
eq0\)).

Step2: Use the point - slope form to find the equation

The point - slope form of a line is \( y - y_1=m(x - x_1) \), where \((x_1,y_1)\) is a point on the line and \( m \) is the slope. We know that \( m = 0 \) and the point \((x_1,y_1)=(-6,-4)\).
Substitute these values into the point - slope form:
\( y-(-4)=0\times(x - (-6)) \)
Simplify the left - hand side: \( y + 4=0\times(x + 6) \)
Since \( 0\times(x + 6)=0 \), we have \( y+4 = 0 \)
Subtract 4 from both sides to get the slope - intercept form (\(y=mx + b\)): \( y=-4 \)

Answer:

\( y=-4 \)