question 1a,b,c,dquestion 2a,b,c,d,e # Educational Resource: Understanding Slope and Graphing Lines## 1. Determine the Slope of Each LineFor each pair of points, calculate the slope of the line or determine if the slope is undefined. Describe if the line rises, falls, is horizontal, or is vertical. Assume \( a, b, \) and \( c \) are positive constants.a. From points \( (4, 5) \) and \((-2, 5)\)b. From points \( \left(\frac{5}{3}, -1\right) \) and \( \left(\frac{5}{3}, -10\right) \)c. From points \( (0, 3) \) and \( (3, 5) \)d. From points \( (a, b) \) and \( (a, b + c) \)## 2. Graph Each of the Following Linesa. \( y = 4 \)b. \( x = -3 \)c. \( y = 2x \)d. \( 4y = -12 \)e. \( x = 0 \)### Graph ExplanationThe graph is a coordinate plane ranging from \(-10\) to \(10\) on both the x and y axes. Each unit is evenly marked, and this graph is used for plotting the lines as specified in the exercise above. 3. For each of the following, find the slope of a line that is parallel to the line given and find the slope of a line that is perpendicular to the line given. a. \( y = 5x \) b. \( y = \frac{1}{3}x - 3 \) c. \( 2x - 3y = 7 \)4. Write an equation for a line that is parallel to \( y = 2x \) and passes through the point \( (4, 2) \).5. Write an equation for a line that is perpendicular to \( y = 2x \) and passes through the point \( (2, 4) \).6. Write an equation for a line that is parallel to \( y = -4x + 1 \) and passes through the point \( (-2, -4) \).7. Write an equation for a line that is perpendicular to \( y = -\frac{3}{2}x + 1 \) and passes through the point \( (1, 2) \).8. Write an equation for a line that is perpendicular to \( y = 1 \) and passes through the point \( (2, 1) \).9. Write an equation for a line that passes through \( (-2, 6) \) and is perpendicular to the line that has an x-intercept of 2 and a y-intercept of 4.

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1. Find the slope of the line passing through each pair of points or state that the slope is undefined. Indicate whether the line rises, falls, is horizontal, or is vertical. Assume a, b and c are positive constants. a. (4, 5) and (-2,5) b. ,-1) and (-10) c. (0,3) and (3,5) d. (a, b) and (a, b + c) 2. **Graph each of the following lines. a. y = 4 b. x = -3 c. y = 2x d. 4y = -12 e. x = 0 -10 -8 -6 -4 10- 8 6 4 2 0 -2 -6 -8 -10- 0 2 6 8 10

1. Find the slope of the line passing through each pair of points or state that the slope is undefined. Indicate whether the line rises, falls, is horizontal, or is vertical. Assume a, b and c are positive constants. a. (4, 5) and (-2,5) b. ,-1) and (-10) c. (0,3) and (3,5) d. (a, b) and (a, b + c) 2. **Graph each of the following lines. a. y = 4 b. x = -3 c. y = 2x d. 4y = -12 e. x = 0 -10 -8 -6 -4 10- 8 6 4 2 0 -2 -6 -8 -10- 0 2 6 8 10

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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question 1a,b,c,d

question 2a,b,c,d,e

# Educational Resource: Understanding Slope and Graphing Lines

## 1. Determine the Slope of Each Line

For each pair of points, calculate the slope of the line or determine if the slope is undefined. Describe if the line rises, falls, is horizontal, or is vertical. Assume \( a, b, \) and \( c \) are positive constants.

a. From points \( (4, 5) \) and \((-2, 5)\)

b. From points \( \left(\frac{5}{3}, -1\right) \) and \( \left(\frac{5}{3}, -10\right) \)

c. From points \( (0, 3) \) and \( (3, 5) \)

d. From points \( (a, b) \) and \( (a, b + c) \)

## 2. Graph Each of the Following Lines

a. \( y = 4 \)

b. \( x = -3 \)

c. \( y = 2x \)

d. \( 4y = -12 \)

e. \( x = 0 \)

### Graph Explanation

The graph is a coordinate plane ranging from \(-10\) to \(10\) on both the x and y axes. Each unit is evenly marked, and this graph is used for plotting the lines as specified in the exercise above.

3. For each of the following, find the slope of a line that is parallel to the line given and find the slope of a line that is perpendicular to the line given.
a. \( y = 5x \)
b. \( y = \frac{1}{3}x - 3 \)
c. \( 2x - 3y = 7 \)

4. Write an equation for a line that is parallel to \( y = 2x \) and passes through the point \( (4, 2) \).

5. Write an equation for a line that is perpendicular to \( y = 2x \) and passes through the point \( (2, 4) \).

6. Write an equation for a line that is parallel to \( y = -4x + 1 \) and passes through the point \( (-2, -4) \).

7. Write an equation for a line that is perpendicular to \( y = -\frac{3}{2}x + 1 \) and passes through the point \( (1, 2) \).

8. Write an equation for a line that is perpendicular to \( y = 1 \) and passes through the point \( (2, 1) \).

9. Write an equation for a line that passes through \( (-2, 6) \) and is perpendicular to the line that has an x-intercept of 2 and a y-intercept of 4.

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