To solve the equation $y = -6x + 5$ by plugging in $x = 0$ and $x = 1$, let's compute the corresponding $y$-values:

Step 1: Plug in $x = 0$

$y = -6(0) + 5 = 0 + 5 = 5$ So, when $x = 0$, $y = 5$.

Step 2: Plug in $x = 1$

$y = -6(1) + 5 = -6 + 5 = -1$ So, when $x = 1$, $y = -1$.

Coordinates for Plotting:

• $(0, 5)$
• $(1, -1)$

Step 3: Graphing the Equation

To graph the line, plot the points $(0, 5)$ and $(1, -1)$, and draw a straight line through them. The slope is $-6$, indicating the line is steep and decreasing.

Would you like a graphical representation of this?

Let me know if you want further explanation, or if you'd like me to plot this graph for you.

Here are 5 follow-up questions:

1. What is the slope of the line, and how does it affect the graph?
2. Can you find the $y$-intercept from the equation?
3. What would the $y$-value be if $x = 2$?
4. How does the negative slope change the direction of the line compared to a positive slope?
5. Could you describe how to graph this line without computing points?

Tip: The slope of the line represents how much $y$ changes for every unit change in $x$. A steep slope (like $-6$) causes a rapid change in $y$.