Graph the line with slope 

−4

 and 

*y*

-intercept 

7

.

To graph the line with slope \( m = -4 \) and \( y \)-intercept \( b = 7 \), we use the slope-intercept form of a linear equation:

\[
y = mx + b
\]

Here:
- \( m = -4 \) is the slope.
- \( b = 7 \) is the \( y \)-intercept.

Thus, the equation of the line is:

\[
y = -4x + 7
\]

### Key steps to graph:
1. Plot the \( y \)-intercept \((0, 7)\).
2. Use the slope \( m = -4 \) to find additional points. The slope means that for every 1 unit increase in \( x \), the \( y \)-value decreases by 4 units.
   - Starting from \((0, 7)\), move 1 unit to the right (increase \( x \)) and 4 units down (decrease \( y \)) to get the point \((1, 3)\).
   - Continue this process to get more points, like \((2, -1)\), etc.

Would you like me to plot the graph for you?

Here are some follow-up questions for practice:
1. What is the general form of a linear equation?
2. How does changing the slope affect the steepness of the line?
3. What would the graph look like if the slope was positive?
4. How do you determine the x-intercept from the equation \( y = -4x + 7 \)?
5. What happens if the y-intercept is negative?

**Tip**: Always check the slope sign; it tells you if the line rises or falls as \( x \) increases.

Graph the line with slope −4 and y-intercept 7.

Learn how to graph the line with a slope of -4 and a y-intercept of 7. This problem demonstrates the use of the slope-intercept form y = mx + b to plot a straight line on a graph. Suitable for students in Grades 7-10.

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