Let's solve each question.

Question 3

We need to find the slope of a line that is parallel to the line given by the equation: $y = \frac{3}{4}x + 2$ In the slope-intercept form $y = mx + b$, $m$ represents the slope. Here, the slope $m$ is $\frac{3}{4}$.

For two lines to be parallel, they must have the same slope. Thus, the slope of the line parallel to this one is also $\frac{3}{4}$.

Answer for Question 3: $\frac{3}{4}$

Question 4

We need to find the slope of a line that is perpendicular to the line given by: $y = -\frac{1}{2}x + 5$ In this equation, the slope $m$ is $-\frac{1}{2}$.

For two lines to be perpendicular, the slopes must be negative reciprocals of each other. The negative reciprocal of $-\frac{1}{2}$ is $2$ (since $-\frac{1}{2} \times 2 = -1$).

Answer for Question 4: $2$

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Related Questions

1. How do you determine the slope of a line given two points?
2. What are the characteristics of perpendicular lines in coordinate geometry?
3. How can we identify if two lines are parallel just by looking at their equations?
4. What is the role of the y-intercept in the slope-intercept form of a line?
5. How do we find the equation of a line passing through a specific point and parallel to another line?

Tip

For perpendicular lines, always remember that their slopes multiply to $-1$ if they are indeed perpendicular.