Overview
The lecture covers how to find and interpret x-intercepts and y-intercepts of a graph using the Cartesian coordinate system, including the necessary steps and example coordinates.
The Cartesian Coordinate System
- The Cartesian coordinate system uses two axes: the x-axis (horizontal) and the y-axis (vertical), meeting at the origin (0, 0).
- Positive x-values go to the right, negative x-values go to the left; positive y-values go up, negative y-values go down.
X-Intercepts
- The x-intercept is where the graph crosses the x-axis.
- At the x-intercept, the y-value is always zero.
- To find the x-intercept, set y = 0 in the equation and solve for x.
- Example: For the point (-3, 0), x = -3 and y = 0, so this is an x-intercept.
Y-Intercepts
- The y-intercept is where the graph crosses the y-axis.
- At the y-intercept, the x-value is always zero.
- To find the y-intercept, set x = 0 in the equation and solve for y.
- Example: For the point (0, 3), x = 0 and y = 3, so this is a y-intercept.
Writing Intercepts as Coordinates
- The x-intercept is written as (x, 0).
- The y-intercept is written as (0, y).
- Every point on the graph is identified by its x and y coordinates.
Procedure to Find Intercepts
- For the x-intercept: Set y = 0, solve for x, and write the answer as (x, 0).
- For the y-intercept: Set x = 0, solve for y, and write the answer as (0, y).
- Plot the intercepts on the graph and connect them to help draw the line.
Key Terms & Definitions
- Cartesian Coordinate System — A grid defined by perpendicular x and y axes intersecting at the origin (0, 0).
- X-intercept — The point(s) where a graph crosses the x-axis (y = 0).
- Y-intercept — The point(s) where a graph crosses the y-axis (x = 0).
- Origin — The point (0, 0) where the x and y axes meet.
Action Items / Next Steps
- Practice finding x- and y-intercepts for different linear equations.
- Plot intercepts on graph paper to visualize graphing lines.