Graph the following line by first determining the gradient and y intercept of the equation:
            
y=2-4x


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.

Graph the following line by first determining the gradient and y intercept of the equation: y = 2 - 4x

Learn how to graph the linear equation y = 2 - 4x by determining the slope and y-intercept. This problem includes key algebraic concepts such as slope-intercept form and the relationship between slope and graph direction. Ideal for students in Grades 7-10.

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