The given equation is:

$y = 2 - 4x$

This equation is already in slope-intercept form, which is:

$y = mx + b$

Where:

• $m$ is the gradient (or slope)
• $b$ is the y-intercept

1. Determine the gradient:

From the equation $y = 2 - 4x$, we can rewrite it as:

$y = -4x + 2$

So, comparing it with $y = mx + b$:

• The slope ($m$) is $-4$.

2. Determine the y-intercept:

The y-intercept ($b$) is the constant term, which is $2$. This means the line intersects the y-axis at the point $(0, 2)$.

3. Graph the Line:

• Step 1: Start by plotting the y-intercept $(0, 2)$.
• Step 2: Use the slope of $-4$. This means for every unit you move right (positive $x$-direction), the value of $y$ decreases by 4 units (downwards).

Another point can be found by moving 1 unit to the right and 4 units down. So, starting from $(0, 2)$, moving to $(1, -2)$ gives another point.

Finally, draw a straight line through these two points.

Would you like me to graph this for you?

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Here are 5 related questions:

1. How would you determine the slope if the equation were in a different form?
2. What does the negative slope tell you about the direction of the line?
3. How would you find the x-intercept of the equation?
4. How does the slope affect the steepness of the line?
5. What changes in the graph if the y-intercept changes?

Tip: The slope of a line indicates its steepness and direction: positive slopes rise as they move right, while negative slopes fall.