Question

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

Explanation:

Step1: Calculate 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 of the line

Using the point - slope form \( y - y_1=m(x - x_1) \), with \( m = 0\) and using the point \((1,2)\), we substitute into the formula: \( y - 2=0\times(x - 1) \), which simplifies to \( y=2 \).

Step3: Graph the line

The line \( y = 2\) is a horizontal line. To graph it, we plot the points \((1,2)\) and \((-1,2)\) (and any other points with \( y = 2\) and different \( x\) - values, like \((0,2)\), \((2,2)\) etc.) and draw a straight line through them. This line is parallel to the \( x\) - axis and passes through all points where the \( y\) - coordinate is 2.

Answer:

The equation of the line is \( y = 2\), and the graph is a horizontal line passing through points with \( y\) - coordinate 2 (e.g., \((1,2)\), \((-1,2)\), \((0,2)\) etc.).