The equation provided is:

$y = -\frac{1}{2}x + 5$

This is a linear equation in slope-intercept form, $y = mx + b$, where:

• $m = -\frac{1}{2}$ is the slope,
• $b = 5$ is the y-intercept.

Y-Intercept:

The y-intercept is the value of $y$ when $x = 0$. From the equation, we can directly see that the y-intercept is $5$, meaning the point $(0, 5)$ is where the line crosses the y-axis.

Graphing the Equation:

1. Plot the y-intercept $(0, 5)$.
2. Use the slope $-\frac{1}{2}$, which means for every 2 units you move to the right along the x-axis, you move 1 unit down (because the slope is negative).
3. Plot another point using this slope, for example, from $(0, 5)$, moving 2 units to the right to $(2, 4)$.
4. Draw a straight line through these points to complete the graph.

Would you like me to provide a visual graph of this? Do you want to ask more questions about the concept?

Related Questions:

1. How do you calculate the slope between two points on a line?
2. What is the significance of the slope being negative in a linear equation?
3. How do you find the x-intercept of a linear equation?
4. Can you explain the steps to graph a line using the slope-intercept form?
5. How would the graph change if the slope was positive?

Tip:

Always double-check your slope and intercept values when graphing to avoid errors in plotting.