Write the equation of the line that passes through the points left parenthesis, minus, 4, comma, 9, right parenthesis(−4,9) and left parenthesis, minus, 1, comma, 9, right parenthesis(−1,9). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.

1 answer

To determine the equation of the line passing through the points \((-4, 9)\) and \((-1, 9)\), we first observe that both points have the same \(y\)-coordinate (9). This indicates that the line is horizontal.

For a horizontal line, the equation can be expressed as:

\[ y = c \]

where \(c\) is the \(y\)-coordinate for all points on the line. Since both points have a \(y\)-coordinate of 9, the equation of the line is:

\[ y = 9 \]

If the question specifically asks for the point-slope form, a horizontal line can also be expressed using the slope and one of the points. The slope \(m\) of a horizontal line is \(0\). The point-slope form is given by:

\[ y - y_1 = m(x - x_1) \]

Using the point \((-4, 9)\) and the slope \(m = 0\):

\[ y - 9 = 0(x + 4) \]

Simplifying this gives:

\[ y - 9 = 0 \]

which simplifies to:

\[ y = 9 \]

In conclusion, the equation of the line in fully simplified point-slope form is:

\[ y = 9 \]

or in point-slope form using one of the points:

\[ y - 9 = 0(x + 4) \]

Both forms express the same horizontal line.