To graph the given equation $y + 1 = 5(x + 2)$, let’s rewrite it into slope-intercept form ($y = mx + b$) and find key points to plot.

Steps:

1. Rewrite the equation: $y + 1 = 5(x + 2)$ Expand and simplify: $y + 1 = 5x + 10$ Subtract 1 from both sides: $y = 5x + 9$

   This is the slope-intercept form where:

   • $m = 5$ (slope),
   • $b = 9$ (y-intercept).

2. Plot the y-intercept: The line crosses the y-axis at $(0, 9)$.

3. Find additional points: Using the slope $m = 5$, rise over run means "go up 5 units and right 1 unit." Starting at $(0, 9)$:

   • Move 1 unit to the right and 5 units up: $(1, 14)$.
   • Or move left 1 unit and down 5 units: $(-1, 4)$.

4. Graph the line: Plot points such as $(0, 9)$, $(1, 14)$, and $(-1, 4)$. Connect these points with a straight line.

Would you like me to calculate more points or clarify further? Let me know!

Relative Questions:

1. What does the slope represent in this graph, and how is it calculated?
2. How do you determine the y-intercept from an equation?
3. Why is the slope-intercept form useful for graphing linear equations?
4. How would you graph this line using intercepts only?
5. Can this method be applied to equations in forms other than slope-intercept?

Tip:

To quickly graph a line, always identify the slope and y-intercept first—they are the easiest points to start with!