To plot the equation $y - 4x = 1$ on a coordinate plane, we will first rewrite the equation in slope-intercept form $y = mx + b$ to make it easier to plot the points:

Step 1: Rewrite the equation in slope-intercept form

$y - 4x = 1$ Add $4x$ to both sides: $y = 4x + 1$

Step 2: Identify points

Now, we have the equation in the form $y = 4x + 1$, where:

• The slope $m = 4$ (which means the line rises 4 units for every 1 unit it moves to the right).
• The y-intercept $b = 1$, which is the point where the line crosses the y-axis at $(0, 1)$.

Step 3: Plot at least two points

1. Start with the y-intercept, $(0, 1)$, because when $x = 0$, $y = 1$.
2. For another point, let's set $x = 1$ and find $y$: $y = 4(1) + 1 = 4 + 1 = 5$ So, the point $(1, 5)$ is another point on the line.

Now, plot these two points on the graph:

• Point 1: $(0, 1)$
• Point 2: $(1, 5)$

You can connect these two points with a straight line. The line will continue infinitely in both directions.

Tip:

To find more points on the line, simply choose other values for $x$ and solve for $y$. For example, if $x = -1$, then $y = 4(-1) + 1 = -4 + 1 = -3$. So, another point would be $(-1, -3)$.

Would you like me to help you with additional points, or explain more about graphing lines? Let me know!

Follow-up Questions:

1. How do you calculate the slope of a line from an equation?
2. What happens if you have a negative slope in a line equation?
3. How can you find the x-intercept of the equation $y = 4x + 1$?
4. How would you graph a vertical line, such as $x = 3$?
5. What does it mean when the slope of a line is zero?

Tip: When plotting lines, it helps to always find the slope and y-intercept first before plotting.