Question

graph the line that passes through the points (1, 2) and (-1, 2) and determine the equation of the line.

Explanation:

Step1: Find the slope

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m = \frac{y_2 - y_1}{x_2 - x_1} \). For points \((1, 2)\) and \((-1, 2)\), we have \( x_1 = 1 \), \( y_1 = 2 \), \( x_2 = -1 \), \( y_2 = 2 \). So \( m = \frac{2 - 2}{-1 - 1} = \frac{0}{-2} = 0 \).

Step2: Determine the equation

A line with slope \( m \) and passing through a point \((x_1, y_1)\) has the equation \( y - y_1 = m(x - x_1) \). Using \( m = 0 \) and the point \((1, 2)\), we get \( y - 2 = 0(x - 1) \), which simplifies to \( y = 2 \).

Step3: Graph the line

The line \( y = 2 \) is a horizontal line passing through all points with \( y \)-coordinate 2. So we plot the points \((1, 2)\) and \((-1, 2)\) and draw a horizontal line through them.

Answer:

The equation of the line is \( y = 2 \), and the graph is a horizontal line through \( y = 2 \).