To graph the line given by the equation:

$y = -\frac{2}{5}x + 5$

we will follow these steps:

Step 1: Identify the Slope and Y-Intercept

• Slope (m): $-\frac{2}{5}$
• Y-Intercept (b): $5$

Step 2: Plot the Y-Intercept

• Start by plotting the y-intercept $(0, 5)$ on the graph.

Step 3: Use the Slope to Find Another Point

• The slope $-\frac{2}{5}$ means that for every 5 units you move to the right (positive direction along the x-axis), you move 2 units down (negative direction along the y-axis).
• From the y-intercept $(0, 5)$, move 5 units to the right and 2 units down to reach the next point: $(5, 3)$.

Step 4: Draw the Line

• Draw a straight line passing through the points $(0, 5)$ and $(5, 3)$.

Would you like me to provide further details or help with plotting?

Related Questions:

1. How do you determine the slope and y-intercept from a linear equation?
2. What is the effect of a negative slope on the direction of a line?
3. How do you find the x-intercept of a line?
4. How do you graph a line when given in a different form, such as standard form?
5. How can we verify that a point lies on the line represented by the equation?

Tip: The slope $-\frac{2}{5}$ means the line descends as it moves from left to right, indicating a negative relationship between $x$ and $y$.