📘intermediate algebra review

key term - Y-axis

Definition

The y-axis is the vertical line on a coordinate plane that represents the vertical or up-and-down dimension. It is used to measure and plot the position of points along the vertical axis of a graph.

5 Must Know Facts For Your Next Test

  1. The y-axis is used to plot the vertical or up-and-down position of points on a coordinate plane.
  2. The y-coordinate of an ordered pair represents the position along the y-axis.
  3. The y-intercept of a linear equation is the point where the line intersects the y-axis.
  4. The y-axis is important for graphing linear inequalities, as it helps determine the region that satisfies the inequality.
  5. The distance formula, which is used to find the distance between two points, includes the difference in y-coordinates as a key component.

Review Questions

  • Explain the role of the y-axis in graphing linear equations in two variables.
    • The y-axis is crucial for graphing linear equations in two variables. The y-coordinate of each point on the graph represents the vertical position of that point, which is determined by the equation's slope and y-intercept. The y-axis allows you to plot the points that satisfy the linear equation and visualize the relationship between the variables.
  • Describe how the y-axis is used in graphing linear inequalities in two variables.
    • When graphing linear inequalities in two variables, the y-axis is used to determine the region of the coordinate plane that satisfies the inequality. The y-coordinates of the points in this region represent the possible values for the variable on the y-axis, given the constraints of the inequality. The y-axis is essential for identifying the half-plane or set of points that make up the solution set for the linear inequality.
  • Analyze the role of the y-axis in the distance and midpoint formulas.
    • The y-axis is a key component of the distance and midpoint formulas. In the distance formula, $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$, the difference in y-coordinates, $(y_2 - y_1)$, represents the vertical distance between two points. Similarly, in the midpoint formula, $\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$, the average of the y-coordinates, $\frac{y_1 + y_2}{2}$, determines the y-coordinate of the midpoint. The y-axis is essential for accurately calculating these geometric properties.