Graphs of Linear Functions

To match a linear equation to its graph, check two things: 1. Y-intercept: Where does the line cross the y-axis? This gives you b. 2. Slope: Is the line going up or down? How steep is it? This gives you m. Quick checks: - Positive slope → line goes up ↗ - Negative slope → line goes down ↘ - Steep line → |m| > 1 - Gentle line → |m| < 1 - m = 0 → horizontal line - b > 0 → crosses y-axis above ori…

Given a graph, you can read: | Feature | How to find it | |---|---| | Y-intercept | Where the line crosses the y-axis | | X-intercept | Where the line crosses the x-axis | | Slope | Pick two clear points, use m = frac{text{rise}}{text{run}} | | Equation | Combine slope + y-intercept: y = mx + b | | f(a) | Find x = a on the x-axis, go to the line, read y | | Solve f(x) = k | Find y = k, go to the…