Graph the line passing through the given point and having the indicated slope. Plot two points on the line. through (9/4 , 2), undefined slope

Verified step by step guidance

1. Recognize that an undefined slope means the line is vertical. A vertical line has the form \(x = a\), where \(a\) is the x-coordinate of every point on the line.
2. Identify the x-coordinate of the given point, which is \(\frac{9}{4}\). Since the slope is undefined, the equation of the line is \(x = \frac{9}{4}\).
3. To graph the line, draw a vertical line passing through \(x = \frac{9}{4}\) on the coordinate plane. This line will go straight up and down through this x-value.
4. To plot two points on the line, choose any two different y-values (for example, \(y = 0\) and \(y = 1\)), and pair them with \(x = \frac{9}{4}\). So the points are \(\left(\frac{9}{4}, 0\right)\) and \(\left(\frac{9}{4}, 1\right)\).
5. Plot these two points on the graph and draw the vertical line through them to complete the graph of the line with undefined slope passing through \(\left(\frac{9}{4}, 2\right)\).

Key Concepts

Undefined Slope

An undefined slope occurs when a line is vertical, meaning it goes straight up and down. This happens because the change in x (horizontal change) is zero, making the slope formula division by zero, which is undefined.

Equation of a Vertical Line

A vertical line passing through a point (x, y) has the equation x = constant, where the constant is the x-coordinate of the point. This means all points on the line share the same x-value.

Plotting Points on a Vertical Line

To plot points on a vertical line, choose different y-values while keeping the x-value constant. For example, if the line passes through (9/4, 2), points like (9/4, 1) and (9/4, 3) lie on the line.