Final answer:
The student's equation is a linear equation that can be graphed by rewriting it in slope-intercept form to identify the slope and y-intercept, plotting the y-intercept, and using the slope to find another point. Finally, a line is drawn through the plotted points.
Step-by-step explanation:
The equation provided by the student, y - 6 = (9/5)(x + 2), is a form of a linear equation. To understand and graph this equation, we can follow certain steps:
- Rewrite the equation in slope-intercept form, which is y = mx + b, where m represents the slope and b is the y-intercept. In this case, we have:
- Add 6 to both sides of the equation to isolate y, which yields y = (9/5)x + 18/5 + 6.
- Now the equation can be written as y = (9/5)x + 48/5, clearly showing the slope (9/5) and the y-intercept (48/5).
- Using these values, plot the y-intercept on the graph.
- From the y-intercept, use the slope to determine another point. Since the slope is 9/5, you can go up 9 units and right 5 units from the y-intercept.
- Plot this new point and draw a line through both points, extending the line across the graph.
The student's equation is now expressed in a form that makes graphing straightforward, showing the rate of change of y with respect to x as well as the initial value of y when x is zero.