To graph the equation $y = -\frac{1}{3}(x - 6) + 2$, let's break it down and identify key elements:

1. Identify the Slope and y-intercept:

• The equation is in point-slope form, $y = m(x - x_1) + y_1$.
• Slope (m): $-\frac{1}{3}$. This means for every unit increase in $x$, $y$ decreases by $\frac{1}{3}$.
• Point (x_1, y_1): $(6, 2)$ is the point from which the line is drawn.

2. Plot the Point:

• Start by plotting the point $(6, 2)$ on the graph.

3. Use the Slope:

• From $(6, 2)$, move 1 unit to the right (increase $x$ by 1) and 1/3 unit down (decrease $y$ by $\frac{1}{3}$).
• This gives the next point at $(7, \frac{5}{3})$.

4. Draw the Line:

• Continue plotting points using the slope, or draw a straight line through the plotted points, extending in both directions.

This graph represents a line with a negative slope, indicating it decreases as $x$ increases. The y-intercept can be found by setting $x = 0$ in the equation, giving $y = -\frac{1}{3}(-6) + 2 = 4$.

Summary:

• Slope: $-\frac{1}{3}$
• Point: $(6, 2)$
• y-intercept: $y = 4$

Would you like any more details or a visualization?

Related Questions:

1. How do you find the y-intercept directly from the equation?
2. What is the general form of a linear equation, and how does it differ from the point-slope form?
3. How would you graph a line if the slope were positive instead of negative?
4. How can you determine the x-intercept from this equation?
5. What does the slope of a line indicate about its steepness and direction?

Tip:

Always remember to check your points by substituting them back into the original equation to ensure accuracy.