📝Practice Screen #11.

Question

Use the Desmos graphing calculator to check your graph
Identify the slope and y intercept. Then, graph the linear equation.

y=-\frac{2}{3}x+6
y=−
2
3​x+6

Begin with
b,the y-intercept:

Move with
m,the slope:

Answer 1

To analyze the linear equation \( y = -\frac{2}{3}x + 6 \), let's identify the slope and the y-intercept.

Step 1: Identify the Y-Intercept (b)

The y-intercept (b) is the point where the line crosses the y-axis. From the equation, we see that:

\[ b = 6 \]

This means the y-intercept is at the point (0, 6).

Step 2: Identify the Slope (m)

The slope (m) is the coefficient of x in the equation. Here, we have:

\[ m = -\frac{2}{3} \]

This means that for every 3 units you move to the right (positive direction of x), you will move 2 units down (negative direction of y).

Step 3: Graph the Equation

1. Plot the Y-Intercept: Start by plotting the y-intercept at (0, 6) on the graph.
2. Use the Slope: From the point (0, 6), move 3 units to the right (to x = 3) and then 2 units down (to y = 4), which gives you the point (3, 4).
3. Plot the Second Point: Plot the point (3, 4) on the graph.
4. Draw the Line: Connect the two points with a straight line, extending it in both directions.

Summary of the Graph

• Y-Intercept: (0, 6)
• Slope: -\(\frac{2}{3}\)
• Points to Plot: (0, 6) and (3, 4)

You can use the Desmos graphing calculator to visualize this equation and confirm the line's direction, slope, and intercept. The line should slope downwards from left to right, consistent with a negative slope.