The equation in the problem is:

$y = -2x + 7$

From this, we can analyze the following:

1. Slope: The slope $m$ is the coefficient of $x$, which is $-2$.

2. y-intercept: The $y$-intercept occurs when $x = 0$. The equation simplifies to $y = 7$, so the $y$-intercept is 7.

3. x-intercept: To find the $x$-intercept, set $y = 0$ and solve for $x$: $0 = -2x + 7 \implies 2x = 7 \implies x = \frac{7}{2}$ So, the $x$-intercept is $\frac{7}{2}$.

4. Graph's Behavior:

   • The slope is negative ($-2$), which means the graph is decreasing.
   • Since the slope is not zero, the graph is neither horizontal nor vertical.

Summary:

• Slope: $-2$
• $y$-intercept: $7$
• $x$-intercept: $\frac{7}{2}$
• The graph is decreasing.

Would you like more details on any of these points?

Here are 5 related questions:

1. How do you find the slope of a line from an equation?
2. What is the significance of the $y$-intercept in a linear equation?
3. How does the slope determine whether a line is increasing or decreasing?
4. How do you calculate the $x$-intercept for any linear equation?
5. What does a horizontal or vertical line look like in slope-intercept form?

Tip: The slope can be visualized as the "steepness" of a line; a negative slope means the line goes down as you move to the right.