Consider the equation y=-52x+2

A line parallel to the above line would have a slope of

A line perpendicular to the above line would have a slope of

The equation provided is:

\[
y = -52x + 2
\]

This is in the slope-intercept form \( y = mx + b \), where:
- \( m \) is the slope,
- \( b \) is the y-intercept.

### Slope of the Given Line:
From the equation, the slope \( m \) is **-52**.

### Parallel Line:
A line that is **parallel** to another line must have the **same slope**. Therefore, a line parallel to the given line will also have a slope of:

\[
m_{\text{parallel}} = -52
\]

### Perpendicular Line:
A line that is **perpendicular** to another line has a slope that is the **negative reciprocal** of the original slope. The negative reciprocal of \(-52\) is:

\[
m_{\text{perpendicular}} = \frac{1}{52}
\]

Thus:
- The slope of a line **parallel** to the given line is **\(-52\)**.
- The slope of a line **perpendicular** to the given line is **\(\frac{1}{52}\)**.

Would you like more details or have any questions?

### Related Questions:
1. How do you determine if two lines are parallel or perpendicular using their slopes?
2. Can you explain why the slopes of perpendicular lines are negative reciprocals?
3. What is the significance of the y-intercept in the slope-intercept form of a line?
4. How would the equation of a line parallel to \(y = -52x + 2\) change if it passes through a different point?
5. Can you find the equation of a line perpendicular to \(y = -52x + 2\) passing through the point \((3, 4)\)?

### Tip:
When two lines are perpendicular, multiplying their slopes will always give \(-1\).

Consider the equation y = -52x + 2. A line parallel to the above line would have a slope of? A line perpendicular to the above line would have a slope of?

Learn how to determine the slopes of lines parallel and perpendicular to y = -52x + 2. This problem covers key algebraic concepts, including the slope-intercept form and the rules for parallel and perpendicular slopes. Suitable for students in Grades 8-10.

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