The equation shown is $y = -5x + 3$, which represents a linear equation in slope-intercept form:

$y = mx + b$

Where:

• $m = -5$ is the slope (rate of change).
• $b = 3$ is the $y$-intercept (where the line crosses the $y$-axis).

Key Observations:

1. Slope ($m = -5$):

   • A negative slope means the line is decreasing.
   • For every $1$ unit increase in $x$, $y$ decreases by $5$ units.

2. Y-Intercept ($b = 3$):

   • The line crosses the $y$-axis at $(0, 3)$.

How to Graph:

1. Plot the $y$-intercept at $(0, 3)$.
2. Use the slope:
   • Move down $5$ units (negative slope).
   • Move right $1$ unit (positive direction for $x$).
   • Plot the next point.
3. Draw a straight line through these points.

Would you like me to:

• Show the steps for plotting this graph in detail?
• Calculate specific points on the line?
• Answer any related questions?

Here are 5 related questions to deepen your understanding:

1. What is the slope of a line parallel to $y = -5x + 3$?
2. What is the slope of a line perpendicular to $y = -5x + 3$?
3. How do you find the $x$-intercept of the equation $y = -5x + 3$?
4. What happens to the graph if the slope changes to $-2$ but the $y$-intercept stays $3$?
5. How do you rewrite $y = -5x + 3$ in standard form $Ax + By = C$?

Tip:

When graphing a line, always start with the $y$-intercept and use the slope (rise/run) to plot additional points.