91Ó°ÊÓ

The slope-intercept form of a linear equation is a way to express the line using the slope and y-intercept. The general formula is \( y = mx + b \). Here, \( m \) is the slope of the line, which tells you how steep the line is, and \( b \) is the y-intercept, the point where the line crosses the y-axis.

For the inequality given, \( x + 5y < -5 \), we need to write it in slope-intercept form. First, isolate \( y \):
\[ x + 5y < -5 \]
Subtract \( x \) from both sides:
\[ 5y < -x - 5 \]
Divide by 5:
\[ y < -\frac{1}{5}x - 1 \]
Now, we see the slope is \( -\frac{1}{5} \) and the y-intercept is \( -1 \). This form makes it easy to graph the inequality by showing the slope and y-intercept directly!

Sh  ...) ). We shade all the area below this line (if you test any point in this area;
for example, (0, 0) and plug it back to all inequalities of y  since (0 <  -1), it confirms our mapped area correctly and therefore shows us wh ... , shading region)}.

Finally, shading is crucial because it visually shows solutions that hold true for all inequality points on the graph. Always use dashed line shading regions, leading students to better understand graphing linear inequalities.