Key Concepts:
- Graphical Representation: A linear function represents a straight line in the coordinate plane.
- Plotting Using Intercepts: A line can be graphed using the x- and y-intercepts found by setting (x = 0) and (y = 0) in the equation.
- The x-intercept is the point where the graph intersects the x-axis ((y = 0)).
- The Slope-Intercept Method: Start from the y-intercept and move according to the slope.
- The slope determines the moving direction (positive = increasing, negative = decreasing).
- Points on a Line: A point ((x, y)) is on a line if, when substituted into the corresponding function, it makes the equation true.
Skills Covered:
- Finding x- and y-intercepts from an equation or a graph.
- Plotting a linear function given its equation.
- Checking whether a point lies on a given line.
Example Problems:
- Find the x- and y-intercepts of (4x - 2y = 8) and graph the line.
- Determine whether the point ((3, 2)) lies on the line given by (y = \frac{1}{2}x + 1).
- Graph the equation (y = -2x + 5) using the slope and y-intercept.