Graph the line passing through the given point and having the indicated slope. Plot two points on the line. through (- 5/2 , 3), undefined slope

Verified step by step guidance

1. Understand that an undefined slope means the line is vertical. Vertical lines have equations of 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 \(\left(-\frac{5}{2}, 3\right)\), which is \(-\frac{5}{2}\).
3. Write the equation of the vertical line passing through this point as \(x = -\frac{5}{2}\).
4. To plot two points on this line, choose any two different y-values and pair them with \(x = -\frac{5}{2}\). For example, points could be \(\left(-\frac{5}{2}, y_1\right)\) and \(\left(-\frac{5}{2}, y_2\right)\), where \(y_1\) and \(y_2\) are any numbers you select.
5. Plot these points on the coordinate plane and draw a vertical line through them, which represents the line with an undefined slope passing through the given point.

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 is zero, making the slope formula (change in y divided by change in x) impossible to calculate. Such lines have equations of the form x = constant.

Equation of a Vertical Line

A vertical line passing through a point has an equation where x equals the x-coordinate of that point. For example, if the point is (-5/2, 3), the line's equation is x = -5/2. This line includes all points with x = -5/2 regardless of their y-values.

Plotting Points on a Vertical Line

To plot points on a vertical line, choose different y-values while keeping the x-value constant. For instance, with x = -5/2, points like (-5/2, 0) and (-5/2, 4) lie on the line. Plotting these helps visualize the vertical line on the coordinate plane.