Question
Graph the line that passes through the points left parenthesis, 1, comma, 2, right parenthesis(1,2) and left parenthesis, minus, 1, comma, 2, right parenthesis(−1,2) and determine the equation of the line.
Answers
GPT-4o mini
To find the equation of the line that passes through the points \((1, 2)\) and \((-1, 2)\), we can first note that both points have the same \(y\)-coordinate of 2. This indicates that the line is horizontal.
The equation of a horizontal line can be written in the form:
\[
y = k
\]
where \(k\) is the \(y\)-coordinate of any point on the line. Since both points we have are at \(y = 2\), the equation of the line is:
\[
y = 2
\]
### Graphing the Line
To graph the line:
1. Draw a set of coordinate axes.
2. Since the line is horizontal and crosses the \(y\)-axis at \(y = 2\), draw a horizontal line that intersects the \(y\)-axis at the point \((0, 2)\).
3. Mark the points \((1, 2)\) and \((-1, 2)\) on the line.
The horizontal line at \(y=2\) will extend infinitely left and right across the graph.
### Summary
The equation of the line that passes through the points \((1, 2)\) and \((-1, 2)\) is:
\[
\boxed{y = 2}
\]
The equation of a horizontal line can be written in the form:
\[
y = k
\]
where \(k\) is the \(y\)-coordinate of any point on the line. Since both points we have are at \(y = 2\), the equation of the line is:
\[
y = 2
\]
### Graphing the Line
To graph the line:
1. Draw a set of coordinate axes.
2. Since the line is horizontal and crosses the \(y\)-axis at \(y = 2\), draw a horizontal line that intersects the \(y\)-axis at the point \((0, 2)\).
3. Mark the points \((1, 2)\) and \((-1, 2)\) on the line.
The horizontal line at \(y=2\) will extend infinitely left and right across the graph.
### Summary
The equation of the line that passes through the points \((1, 2)\) and \((-1, 2)\) is:
\[
\boxed{y = 2}
\]