The equation $y = -2x + 7$ represents a linear function in slope-intercept form, where:

• The slope (or gradient) $m$ is $-2$.
• The y-intercept $b$ is $7$.

Here's a breakdown of the properties:

1. Slope: The slope is $-2$, meaning for every unit increase in $x$, $y$ decreases by 2 units. This indicates a downward-sloping line.

2. Y-Intercept: The y-intercept is $7$, which is the point where the line crosses the $y$-axis. Therefore, when $x = 0$, $y = 7$.

3. X-Intercept: To find the x-intercept, set $y = 0$: $0 = -2x + 7$ Solving for $x$, we get: $2x = 7 \Rightarrow x = \frac{7}{2} = 3.5$ So, the x-intercept is $(3.5, 0)$.

4. Graph: This line will pass through the points $(0, 7)$ and $(3.5, 0)$.

Would you like to see a graph of this line, or do you have any questions?

Follow-Up Questions

1. How do you find the slope between two points?
2. What is the importance of the y-intercept in a linear equation?
3. How do you convert a linear equation from slope-intercept form to standard form?
4. What does a negative slope indicate about the direction of the line?
5. How can you determine if two lines are parallel?

Tip:

To quickly graph a line, plot the y-intercept first, then use the slope to find another point.